I made croissants once before from the recipe on Bread Cetera. They were great, but Cerinthus said they were not fluffy enough. I hope that these will work out better so I can make some the next time I see him.
Poolish:
100g All-Purpose Flour
100g Water (75 degrees F)
3g dry active yeast
Levain
1 tablespoon mature starter
110g All-Purpose Flour
110g Water (80 degrees F)
Final Dough
225g Milk (Whole Milk?)
150 Levain
200g Poolish
500g Bread Flour
14g Salt
42.5g Sugar
5g Active Dry Yeast
200g Butter
1/4 cup all purpose flour
Egg Wash
1 large egg (or 1 egg yoke and 1 tsp heavy cream)
Directions
Day 1:
Mix the poolish in a bowl. Let sit for 3-4 hours between 75-80 degrees F (or overnight at cool room temperature 65-70 degrees F).
Make the levain in a bowl and Let sit for 3-4 hours between 75-80 degrees F (or overnight at cool room temperature 65-70 degrees F).
Both mixtures are ready when the pass the float test.
Day 2:
Stir the poolish and the levain into a bowl with the milk.
Then add the flour, salt, sugar, and yeast. Mix until no dry spots of flour remain. The easiest way to ensure this is to mix by hand.
Transfer the dough to a plastic bag, press to flatten it into a rectangle and chill in the refrigerator for 2-3 hours.
Sprinkle the butter with flour and pound it into into a flat rectangle about 4x6 inches.
Put the butter on parchment or wax paper and cool, but not so cold that it has to be pounded again.
Once the 2-3 hour wait is over, place the dough on a floured surface and roll it out to a rectangle of 6 by 10 inches. Place the butter in the center of the dough and fold it like a letter over the butter. Re-roll it into the same sized rectangle with a rolling pin. this is called a "turn."
Refrigerate the dough for an hour and then do a second turn.
Refrigerate the dough for an hour and do a third turn. You can let the dough stay in the refrigerator overnight or work with it after 1-2 hours in the freezer.
After the resting period, roll the dough into a 9x12 inch rectangle, approximately 1/2 inch thick. Cut the rectangle into 6-8 equal sized triangles.
Roll up each triangle and arrange them on parchment-lined baking sheets. wrap the sheets loosely with plastic wrap and either let sit at 75-80 degrees F for 2 hours or put in the refrigerator overnight.
Day 3:
Pre heat the oven to 425 degrees F.
Take the croissants out 20 minutes before baking and brush with the egg wash.
Bake until the croissants are a deep golden brown, crisp, and flakey, which should take about 30 minutes. Eat immediately.