1. Make the dough: Stir yeast, water, and 1 teaspoon sugar in a bowl. Let stand until foamy, about 5 minutes. Butter a large bowl; set aside. Put bread flour, all-purpose flour, remaining 3 tablespoons plus 2 teaspoons sugar, and the salt into the bowl of an electric mixer fitted with the dough hook; mix on low speed until combined. Add yeast mixture, milk, and butter; mix until dough just comes together.

2. Knead dough: Scrape dough out onto a lightly floured work surface. Using lightly floured hands, knead until smooth, about 3 minutes. Transfer to buttered bowl, turning to coat.

3. Let dough rise: Cover dough with plastic wrap; transfer to the refrigerator. Let rise until doubled in bulk, about 2 hours (dough should not spring back when you press it with your finger).

4. Make the butter package: About 45 minutes after the dough begins rising, put flour and butter into the clean bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until well combined, 3 to 4 minutes. Scrape butter mixture out onto a piece of parchment paper; shape into a rectangle. Top with parchment, and roll out to an 8-by-10-inch rectangle. Transfer to a baking sheet, and refrigerate 30 minutes.

5. Roll out dough: Turn out dough onto a lightly floured work surface; shape into a rectangle. Roll out to a 10 1/2-by-16-inch rectangle, about 1/2 inch thick, with short side facing you.

6. Place butter package on dough: The butter package should be cool but pliable; your finger should leave an indentation but the butter should still hold its shape. If too soft, continue to refrigerate; if too firm, let stand at room temperature briefly. Place horizontally on bottom half of dough; remove parchment. Fold top half of dough over butter package, and pinch edges of dough to seal.

7. Roll in butter: Turn dough so that a short side is facing you and the seam is on the right. Roll out to a 10-by-20-inch rectangle, about 1/2 inch thick (keep the corners as square as possible).

8. Fold dough into thirds: Remove any excess flour with a pastry brush. Starting at the far end, fold rectangle in thirds as you would a business letter (this completes the first of 3 "turns").

9. Mark dough: Mark the dough with your knuckle (later, this will help you remember how many turns have been completed). Wrap dough in plastic, and refrigerate 1 hour.

10. Repeat process: Remove from refrigerator, and press the dough; it should be pliable but have some resistance. If too soft, return to refrigerator; if too firm, let stand at room temperature, 5 minutes. Repeat the preceding three steps to complete two more turns (make 2 marks for the second turn and 3 marks for the third turn); always start with a short side facing you and the seam on the right, rolling lengthwise before crosswise. After the second turn, wrap dough in plastic, and refrigerate 1 hour. After the third and final turn, wrap dough in plastic, and refrigerate 8 hours (or overnight).

11. Roll out and chill dough: Turn out dough onto a lightly floured work surface, and roll out to a 30-by-16-inch rectangle. If dough becomes unmanageable, cut in half crosswise, and roll out two 15-by-16-inch rectangles (refrigerate 1 piece as you work with the other). Chill in freezer 15 minutes. Remove dough, and remeasure: It should match original dimensions; if not, roll out again. If dough becomes too warm or elastic, chill in freezer, 15 minutes.

12. Cut dough: Cut dough into two 30-by-8-inch rectangles (or four 15-by-8-inch rectangles). Stack rectangles, lining up edges (if you have four smaller rectangles, make two stacks).

13. Trim dough and cut into triangles: Using a pastry or pizza wheel and cutting at a 20-degree angle, trim a small wedge from one short side to create an angled side. Cut dough into triangles, each with a 4 1/2-inch base. You should have about 20 total.

14. Cut slits: Cut a 1-inch slit in the middle of the base of each triangle. Separate the stacks, transferring half the triangles to a parchment-lined baking sheet; cover, and refrigerate.

15. Begin shaping croissants: Working with one triangle at a time and keeping remaining triangles covered with a clean kitchen towel, hold the two corners of the base, and stretch to lengthen it slightly. Grasp inner corners formed by the slit in the base, and lift and stretch them toward the outer sides of the triangle; press to seal.

16. Roll croissants: Using your fingertips, roll the base of the triangle up and away from you, stretching the dough slightly outward as you roll to elongate the point (when finished, the point should be tucked under the croissant).

17. Finish shaping croissants: Bend the two ends toward you to form a crescent shape (the ends should almost touch). Transfer to parchment-lined baking sheets, spacing croissants 2 inches apart. Repeat with remaining triangles. Cover loosely with plastic wrap, and let stand in a warm place until croissants have doubled in bulk and are very soft, 1 1/2 hours to 2 1/4 hours, depending on the temperature of room.

18. Brush with egg: Preheat oven to 400 degrees, with racks in upper and lower thirds. Brush tops of croissants with egg. Bake, rotating sheets halfway through, until croissants are puffed and golden brown, 20 to 25 minutes. Let cool slightly on sheets on wire racks. Serve warm or at room temperature.