For the sponge:
1/4 teaspoon active dry yeast
3/4 cup warm water
2 cups (9 ounces by weight) all-purpose flour
For the croissant dough:
1/4 cup warm water
3/4 cup milk
6 tablespoons sugar
2 packages (4 1/2 teaspoons) active dry yeast
2 1/2 cups (11 1/4 ounces by weight) all-purpose flour
1 tablespoon salt
1 3/4 ounces unsalted soft butter
10 ounces unsalted butter, chilled
1 egg for egg wash
For the sponge:
In an electric mixing bowl, stir the warm water and yeast together. Allow to foam for 5 minutes.
Mix in the flour at low speed. The dough will be sticky. Cover and let rest for 12 hours at room temperature.
For the croissant dough: In a mixing bowl, combine water, milk, and 1 teaspoon of sugar.
Stir in the yeast to dissolve and allow to foam for about 3 minutes. Add the remaining sugar, flour, salt, soft butter and the sponge. Knead with the dough hook for about 10 to 12 minutes. (If working by hand, knead for 15 minutes.)
Transfer dough to a lightly oiled bowl. Cover with plastic wrap and allow to double in bulk in a draft-free area at room temperature, about 1 hour.
On a lightly floured surface, roll the dough into a rectangle 12 by 14- inches. Place the dough rectangle on a baking sheet. Cover with plastic and freeze for about 30 minutes to get the consistency of chilled butter. Roll the 10 ounces of chilled butter between plastic sheet to form a rectangle 12 by 7 inches.
Square up rectangle with a spatula or dough scraper. Position the butter rectangle on one side of the dough. Fold the rest of dough over butter and seal edges to seal in butter. Roll out the dough into a 10 by 20-inch rectangle. Fold one-third of the dough towards the center. Fold the other third over the two layers. Wrap the dough in plastic and refrigerate 30 minutes.
Repeat the rolling and folding process twice more and chill. Finally, on a floured surface, roll the dough into a 19 by 25-inch rectangle. Cut the dough into 20 even triangles.
Use a template for accurate measurements. To roll the crescents, start at the base and roll towards the tip. Finish the roll so that the tip is underneath the croissant.
Curve the end of each croissant and brush with egg wash. (May be frozen at this time). Arrange croissant on a baking sheet lined with parchment.
Let them rise uncovered at room temperature or until doubled in bulk. Bake the croissants at 375 degrees for 18 to 20 minutes.