1 lb. 2 oz. (4 cups) unbleached all-purpose flour; more for rolling
5 oz. (1/2cup plus 2 Tbs.) cold water
5 oz. (1/2 cup plus 2 Tbs.) cold whole milk
2 oz. (1/4 cup plus 2 Tbs.) granulated sugar
1-1/2 oz. (3 Tbs.) soft unsalted butter
1 Tbs. plus scant 1/2 tsp. instant yeast
2-1/4 tsp. table salt
For the butter layer
10 oz. (1-1/4 cups) cold unsalted butter
For the egg wash
1 large egg
Combine all of the dough ingredients in the bowl of a stand mixer fitted with the dough hook. Mix on low speed for 3 minutes, scraping the sides of the mixing bowl once if necessary. Mix on medium speed for 3 minutes. Transfer the dough to a lightly floured 10-inch pie pan or a dinner plate. Lightly flour the top of the dough and wrap well with plastic so it doesn’t dry out. Refrigerate overnight.
Make the butter layer
The next day, cut the cold butter lengthwise into 1/2-inch-thick slabs. Arrange the pieces on a piece of parchment or waxed paper to form a 5- to 6-inch square, cutting the butter crosswise as necessary to fit. Top with another piece of parchment or waxed paper. With a rolling pin, pound the butter with light, even strokes. As the pieces begin to adhere, use more force. Pound the butter until it’s about 7-1/2 inches square and then trim the edges of the butter. Put the trimmings on top of the square and pound them in lightly with the rolling pin. Refrigerate while you roll out the dough.
Laminate the dough
Unwrap and lay the dough on a lightly floured work surface. Roll into a 10-1/2-inch square. Brush excess flour off the dough. Remove the butter from the refrigerator—it should be pliable but cold. If not, refrigerate a bit longer. Unwrap and place the butter on the dough so that the points of the butter square are centered along the sides of the dough. Fold one flap of dough over the butter toward you, stretching it slightly so that the point just reaches the center of the butter. Repeat with the other flaps . Then press the edges together to completely seal the butter inside the dough. (A complete seal ensures butter won’t escape.)
Give the dough a third rolling and folding. Put the dough on the baking sheet and cover with plastic wrap, tucking the plastic under all four sides. Refrigerate overnight.
Divide the dough
The next day, unwrap and lightly flour the top and bottom of the dough. With the rolling pin, “wake the dough up” by pressing firmly along its length—you don’t want to widen the dough but simply begin to lengthen it with these first strokes. Roll the dough into a long and narrow strip, 8 inches by about 44 inches. If the dough sticks as you roll, sprinkle with flour. Once the dough is about half to two-thirds of its final length, it may start to resist rolling and even shrink back. If this happens, fold the dough in thirds, cover, and refrigerate for about 10 minutes; then unfold the dough and finish rolling. Lift the dough an inch or so off the table at its midpoint and allow it to shrink from both sides—this helps prevent the dough from shrinking when it’s cut. Check that there’s enough excess dough on either end to allow you to trim the ends so they’re straight and the strip of dough is 40 inches long. Trim the dough.
Using a paring knife or a bench knife, make a 1/2- to 3/4-inch-long notch in the center of the short side of each triangle. The notch helps the rolled croissant curl into a crescent. Hold a dough triangle so that the short notched side is on top and gently elongate to about 10 inches without squeezing or compressing the dough—this step results in more layers and loft.
Make the egg wash by whisking the egg with 1 tsp. water in a small bowl until very smooth. Lightly brush it on each croissant
Refrigerate the remaining egg wash (you’ll need it again). Put the croissants in a draft-free spot at 75° to 80°F. Wherever you proof them, be sure the temperature is not so warm that the butter melts out of the dough. They will take 1-1/2 to 2 hours to fully proof. You’ll know they’re ready if you can see the layers of dough when the croissants are viewed from the side, and if you shake the sheets, the croissants will wiggle. Finally, the croissants will be distinctly larger (though not doubled) than they were when first shaped.
Shortly before the croissants are fully proofed, position racks in the top and lower thirds of the oven and heat it to 400°F convection, or 425°F conventional. Brush the croissants with egg wash a second time. Put the sheets in the oven. After 10 minutes, rotate the sheets and swap their positions. Continue baking until the bottoms are an even brown, the tops richly browned, and the edges show signs of coloring, another 8 to 10 minutes. If they appear to be darkening too quickly during baking, lower the oven temperature by 10°F. Let cool on baking sheets on racks.