Croissants

Method

1. In the bowl of a stand mixer fitted with a dough hook attachment, mix the milk and yeast together on low speed to dissolve the yeast, about 5 to 10 seconds. Add the all-purpose flour, cake flour, salt, sugar, and 2 tablespoons soft butter, and mix until the butter is mixed in and the dough is smooth, 3 to 4 minutes. Remove the dough from the mixer bowl, place it on a tray, and cover it loosely with plastic wrap. This dough block is called the détrempe. Place the détrempe in the refrigerator for at least 6 hours and up to 12 hours. This allows the dough to firm up and the yeast to take some action and proof a bit.
2. The next day, on a well-floured work surface, press the détrempe down firmly into a square roughly 9 x 9 inches. Rotate the square so that, as you face it, it looks like a baseball diamond and then use the sides of your palm to mark a 7-inch square in the middle of the diamond, creating triangle-ish flaps at the corners.
3. Roll out these triangle flaps as best as you can into square-ish shapes (about 4-inch squares)—you will have to tug a bit at the edges to pull them into a square shape as you are rolling. When you are done the entire piece of dough will be about 15×15 inches, with a 7×7 inch square lump in the middle and 4 square-ish flaps off of each side of that lump. The 7-inch square lump will be about 1 inch thick and the 4 square-ish flaps will be roughly ¼- inch thick.
4. Pound the cold butter with a rolling pin to soften it and shape it into a 7-inch square, alternatively, place the cold butter in the bowl of a stand mixer fitted with a paddle attachment and beat for 15 to 20 seconds on medium speed to break up the butter while still keeping it quite cold. Remove the butter from the bowl and scrape it out directly onto the 7-inch square lump in your dough, patting it with your fingers to shape it into a square shape that covers the 7-inch square. The butter should be about the same consistency as the dough.
5. Fold 1 of the flaps up and stretch it over the butter square to cover it entirely. (The dough is quite stretchy, so you can stretch it to cover the butter completely.) Fold and stretch a second flap over that; repeat with third and then the fourth flap. Tug at the flaps to keep them in a square shape that covers the butter. You will now have a butter square that is entirely encased in dough above and below. Using the palms of both hands, firmly press this dough package down into a square roughly 9 x 9 inches.
6. When the dough package is relatively flat, switch to a rolling pin and continue to flatten the dough by pressing up and down on the package with the pin. Roll it out into a rectangle about 18 inches wide and 10 inches tall. Flour the dough and the work surface generously as needed to prevent the rolling pin from sticking to the dough.
7. When rolling out laminated dough, your goal is to keep the layers directly on top of one another and even, to preserve the layering. In between turns you have three layers of dough one on top of another. Rather than immediately rolling these out with a back and forth motion, first flatten the dough with your rolling pin by firmly pressing down on the dough and then moving your rolling pin up and down and pounding along the length of the dough—use your rolling pin to create ridges as it compacts the dough. Once the dough is pressed down all over, then use the pin to roll back and forth, smoothing out the ridges while flattening and rolling the dough into the shape you want. By pressing down first before rolling, you preserve the layers. If you were to start rolling immediately after folding the dough the very top layer would take all the pressure from the rolling pin and stretch out way over the very bottom layer. Using this technique to compress the dough first helps to keep the layers even, making for a more-flaky end product.
8. Once you have a dough rectangle about 18 x 10 inches, lightly score the rectangle in half with a bench scraper or a knife. (This will be a 10-inch line from top to bottom.)  Brush any loose flour off the dough. Take the right side of the dough and fold it in so the right edge of the dough meets the line you scored in the center. Then take the left side of the dough and fold that in so the left edge meets the center line as well, meeting the right edge. Square off the folds as much as you can so that they meet entirely in the middle, and then fold the right half of the dough on top of the left half. This is called a book fold. Your dough will now be 4 to 5 inches wide, 10 inches from top to bottom, and about 2 inches thick. Rotate the dough 45 degrees clockwise so that now it is 10 inches side to side and 4 to inches up and down. The process of folding and rotating is called turning the dough.
9. Now roll the dough into a rectangle about 21 inches wide and 8 inches tall. The dough might be a little sticky so, again, be sure to flour the dough and the work surface as needed to prevent the pin from sticking. This time lightly score the rectangle into thirds with a bench scraper or a knife, each third 6 to 7 inches wide and still 8 inches top to bottom. Brush any loose flour off the dough. Take the right third of the dough and flip it over onto the middle third. Then take the left third of the dough and flip that third on top of the middle and right thirds. (This is like folding a business letter.) Your dough should now be about 7 inches wide, 8 inches top to bottom and about 2 inches thick. Rotate the dough pile 45 degrees clockwise so that now it is 8 inches side to side and 7 inches up and down.
10. Place the dough on a baking sheet and cover it completely with plastic wrap, tucking the plastic under the dough as if you’re tucking it into bed. Place the dough in the refrigerator for at least 1 ½ hours and no more than 3 hours.
11. Remove the dough from the refrigerator and place it on a well-floured work surface with the long side of the rectangle facing you. This time roll the dough into a rectangle about 18 inches wide and 12 inches tall. Give it another business letter fold (score the rectangle into thirds, fold the right third onto the middle third and fold the left third on top of that). Again place the dough on a baking sheet and cover it completely in plastic. This time let it rest in the refrigerator for at least 4 hours and up to 16 hours.
12. Line a baking sheet with parchment paper.
13. Remove the dough from the refrigerator and place it on a well-floured work surface again with the long side of the rectangle facing you. Roll it out into a long skinny rectangle about 30 inches wide and 6 to 7 inches tall.
14. Starting at the bottom left corner of the rectangle, mark along the bottom edge of the rectangle every 5 inches until you get to right side of the dough. Then starting at the top left corner of the rectangle, mark along the top edge exactly midway between the notches on the bottom edge—so your first notch will be about 2 ½ inches from the left and then you’ll continue to notch every 5 inches. Use a sharp chef’s knife to cut the dough rectangle into triangles by cutting diagonally from notch to notch. You will end up with 10 triangles and a few edge pieces of scrap.
15. Cut a 1-inch slit in the center of the base of each triangle. Turn all of the triangles so they are oriented with the base on top and the triangle point pointing down toward you. Pick up a triangle and hold it by its base with one hand and gently stretch it and stroke it lengthwise with your other hand to elongate it to 10 to 12 inches in length.
16. Place the lengthened triangle on the work surface, fan open the base at the 1-inch slit into a Y, and then roll the dough down to the point. Once you roll down to the point, place the croissant on the parchment-lined baking sheet, with the point side down, touching the parchment. Continue with all the dough triangles, spacing the croissants 2 to 3 inches apart on the baking sheet.
17. Cover the croissants with plastic wrap and leave them in a warm place for 2 to 2 ½ hours until they are somewhat poufy and airy. Whisk the egg in a small bowl and use a pastry brush to brush egg wash lightly on all the croissants.
18. If you are baking the croissants the same day, cover them again with plastic wrap and let them finish proofing for another 30 minutes to 1 hour. They will get even more poufy and jiggly when you nudge them.
19. Heat oven to 400°F.
20. When the croissants are done proofing, egg wash them again. Bake at 400°F for the first 5 minutes and then turn the oven down to 350°F and bake for another 25 to 35 minutes (for a total baking time of 30 to 40 minutes) until they are golden brown all over.
21. If you are baking the croissants the next day, wrap them in plastic wrap and place them in the refrigerator. The next morning, remove the croissants from the fridge and let them sit at room temperature for 30 to 40 minutes.
22. Heat oven to 400°F.
23. Give the croissants a second egg wash and bake at 400°F for the first 5 minutes and then turn the oven down to 350°F and bake for another 25 to 35 minutes (for a total baking time of 30 to 40 minutes) until they are golden brown all over.
24. Croissants are best enjoyed the same day. If you want to store them in an airtight container overnight, refresh them in a 300°F oven for 5 to 8 minutes before serving.