Mix the pre-ferment:
In a mixing bowl, stir the warm water and yeast together. Wait for them to foam, about 2 minutes. Add the flour and mix on low speed for 3 minutes with a mixer (or for about 5 minutes by hand). The dough will be sticky and somewhat lumpy. Cover and let rest at room temperature (75°F) for 12 hours, until tripled in bulk.
Make the dough:
In a small pan or bowl, combine the water and milk. Pour the liquid into a large mixing bowl and add 1 teaspoon of the sugar. Sprinkle the yeast over the warm liquid, stir to dissolve, and let sit until it starts to foam, about 2 minutes.
Add the flour, the remaining sugar, the salt, and the softened butter, along with the pre-ferment, and mix. If using a stand mixer, knead with the dough hook, stopping to push the dough down the hook. Knead until the dough pulls into a translucent sheet without tearing, about 12 minutes. (If working by hand, knead for about 15 minutes.) The dough will be soft and supple.
Transfer the dough to a large, lightly oiled bowl and cover with plastic. Let rise at room temperature (avoid a drafty place) until doubled in bulk, about 1 hour.
Roll out the dough:
On a lightly floured surface, roll the dough into a 12x14-inch rectangle that’s 1/2 inch thick.
Transfer the dough to a baking sheet, brushing off any excess flour. Cover it with plastic and put it in the freezer until it’s as firm as chilled butter, about 30 minutes.
Pound the butter to make it pliable:
Five minutes before the dough is finished chilling, lay the cold butter between layers of plastic wrap or freezer bags. With a rolling pin, pound the butter into a 12x7-inch rectangle that’s uniformly thick. Even out and square up the rectangle with your fingers and a dough scraper.
Seal the butter in the dough:
On a lightly floured surface, position the pounded butter on one side of the dough rectangle, lining it up parallel with the edges and leaving about 1/4-inch margin. Fold the rest of the dough over the butter. Pinch the edges to seal in the butter. Fold the pinched edges over.
Position the dough rectangle with the folded edge away from you. Roll the dough into a 10x20-inch rectangle that’s 1/2 inch thick.
Fold and roll to make flaky layers
Fold one-third of the dough toward the center, brushing off excess flour as you go. Fold the other third over the two layers, brushing off flour as needed. Press an indentation in the dough after each turn to remind you how many turns you’ve made (at this point, just one). Wrap the dough in plastic and refrigerate for at least 30 minutes to let the gluten relax and the butter firm up.
Remove the dough from the refrigerator, position it horizontally, and roll it out to a 10x20-inch rectangle. Fold, rewrap, and chill as before. Repeat this sequence once more.
Shape and bake the croissants:
Let the dough rest for 1/2 hour, then roll it into a 19x25-inch rectangle that’s 1/8 inch thick. Trim ragged edges and slice the dough in half horizontally, leaving both halves in place.
On the upper edge of the top strip, measuring from the left corner, cut small notches every 4-1/2 inches. On the lower edge of the bottom strip, do the same thing. With a pizza cutter and a ruler, connect the upper left corner of the top strip to the first notch on the bottom strip. Continue, making parallel diagonal lines. Now connect the lower left corner of the bottom strip to the first notch on the top strip to cut a triangle; continue until you end up with 20 triangles and some scraps.
Cut a small notch in the middle of each triangle base and dab the three corners with egg wash. The notch helps the rolled croissant curl into a crescent. Starting at the base of the triangle, pull gently so the notch separates. Fold the base over twice, 1/2 inch each time, pinching as you go.
Roll towards the tip with your dominant hand, pulling gently at the tip with your other hand. Finish the roll so that the tip is underneath the croissant. Turn it so that the lines of the roll converge toward you, and set the croissant on a parchment-lined baking sheet; leave at least 1 inch between croissants.
Gently curve the ends of each croissant together toward you, pinch, and brush the croissants with egg wash. (If you’re freezing the croissants, do it now.) Let them rise uncovered at room temperature until doubled in bulk, about 1 hour. Heat the oven to 375°F. Bake the croissants in the hot oven for 18 to 20 minutes or until golden brown. To check for doneness, push gently on the inner curve of the croissant. If it springs back, the croissant is thoroughly baked.
Make Ahead Tips
Shaped, unbaked croissants can be frozen on a baking sheet, then wrapped in plastic wrap and frozen. To bake frozen croissants, take them out of the freezer the night before and defrost them, uncovered, in the refrigerator. The next morning, let them rise at room temperature until almost doubled in bulk (1 to 2 hours) before baking.
nutrition information (per serving):
Photo: Daniel Proctor