French for "crust," a croustade is usually made with flaky pastry. Here, the buttery dough is filled with fruit jam for the ultimate breakfast treat.
Dough: In a small bowl, sprinkle yeast over milk; stir until dissolved. Let sit until foamy, about 5 minutes. Stir in vanilla seeds. In the bowl of a mixer fitted with the dough-hook attachment, mix together 4 1/2 cups flour, sugar, salt, and 1/2 stick butter on low speed until butter is incorporated and mixture resembles coarse meal, 3 to 4 minutes. Add yeast mixture; mix until dough just comes together. Add eggs and yolk; mix until just combined, 2 to 3 minutes (do not overmix).
Turn dough out onto a lightly floured surface, making sure to include any loose bits left at bottom of bowl. Gently knead to form a smooth ball, about 30 seconds. Wrap tightly in plastic; refrigerate at least 2 hours and up to overnight.
In the bowl of a mixer fitted with the paddle attachment, beat together remaining 3 1/2 sticks butter and 2 tablespoons flour. Shape mixture into a 12-by-10-inch rectangle on a piece of plastic wrap. Refrigerate 15 minutes or up to 1 day. On a lightly floured surface, roll out dough to an 18-by-10-inch rectangle, a little over 1/4 inch thick, keeping the corners as square as possible. Remove any excess flour with a dry pastry brush. Remove butter mixture from refrigerator and let stand at room temperature until it is the same consistency as the dough. With a short side facing you, place butter mixture over two-thirds of the dough. Fold the unbuttered third over as you would a business letter, followed by the remaining third. This seals in the butter.
Roll out dough again to an 18-by-10-inch rectangle, then fold into thirds as described above; refrigerate 1 hour. This completes the first of three turns. Repeat rolling and folding process two more times, refrigerating at least 1 hour between turns. To help you remember how many turns have been completed, mark the dough after each one: make one mark for the first turn, two for the second, and three for the third.
Wrap tightly in plastic and refrigerate at least 4 hours and up to overnight. Dough can also be frozen, tightly wrapped in plastic, up to 2 weeks (thaw in refrigerator overnight before using).
On a lightly floured surface, roll out dough to a 20-by-16-inch rectangle, trimming edges if necessary. Using a ruler, cut into twenty 4-inch squares and transfer to one of three parchment-lined baking sheets, leaving an even amount of space between squares until you have two sheets with 7 squares each, and one sheet with 6 squares.
Working with one square at a time, fold in half to form a triangle. Using a sharp pizza wheel, make a cut parallel to one of the short sides of the triangle, about 1/4 inch from the edge, stopping about 1/8 inch from the opposite short side. Make a second cut parallel to the opposite short side, about 1/4 inch from the edge, stopping about 1/8 inch from the first line. (Make sure lines do not meet.) Unfold triangle back into a square and brush egg wash along edges. Fold outer cut corners over to opposite inside corners. Press borders down to seal. Repeat with remaining squares. Loosely cover with plastic wrap and let rise in a warm spot until doubled in bulk, about 1 hour.
Filling: Preheat oven to 375 degrees. Fill center of each square with 1 tablespoon jam, then lightly brush dough with egg wash. Bake, rotating sheets from top to bottom halfway through, until deep golden brown, 20 to 25 minutes. Let cool completely. Pastries are best served the same day.