Make the pastries
Using a stand mixer fitted with the paddle attachment (or a handheld mixer), mix together the flour, sugar, and salt for 10 to 15 seconds, or until combined. Scatter the butter over the top. Mix on low speed for 1 to 11/2 minutes, or just until the flour is no longer bright white and holds together when you clump it and lumps of butter the size of pecans are visible throughout.
In a small bowl, whisk together the egg yolks and milk until blended. Add to the flour mixture all at once. Mix on low speed for about 30 seconds, or until the dough just barely comes together. It will look really shaggy and more like a mess than a dough.
Dump the dough out onto an unfloured work surface, then gather it together into a tight mound. Using your palm and starting on one side of the mound, smear the dough bit by bit, starting at the top of the mound and then sliding your palm down the side and along the work surface until most of the butter chunks are smeared into the dough and the dough comes together. Do this once or twice on each part of the dough, moving through the mound until the whole mess has been smeared into a cohesive dough with streaks of butter.
Gather up the dough, wrap tightly in plastic wrap, and press down to flatten into a disk about 1 inch thick. Refrigerate for at least 4 hours before using. (The dough will keep in the refrigerator for up to 4 days or in the freezer for up to 1 month).
When you're ready to use the dough, position a rack in the center of the oven, and heat the oven to 350°F.
Remove the dough from the refrigerator and divide it in half. Press each half into a rectangle. On a lightly floured surface, roll out each half into a 14-by-11-inch rectangle. Using a paring knife, lightly score 1 rectangle into eight 3-1/2-by-5-1/2-inch rectangles (about the size of an index card).
Brush the top surface of the entire scored rectangle with the egg. Spoon 2 Tbs. of the jam in a mound in the center of each scored rectangle. Lay the second large dough rectangle directly on top of the first. Using fingertips, carefully press down all around each jam mound, so the pastry sheets adhere to each other.
Using a knife, a pizza roller (easier), or a fluted roller (easier and prettier), and following the scored lines, cut the layered dough into 8 rectangles. Place the rectangles, well spaced, on a baking sheet.
Bake for 40 to 45 minutes, or until the tops of the pastries are evenly golden brown. Let cool on the baking sheet on a wire rack for about 30 minutes.
Make the glaze
While the pastries are cooling, in a small bowl, whisk together the confectioners’ sugar, vanilla, and enough of the water to make a smooth, pourable glaze. You should have about 1/2 cup.
When the pastries have cooled for 30 minutes, brush the tops evenly with the glaze, then sprinkle with the rainbow sprinkles (if using). Let stand for 10 to 15 minutes to allow the glaze to set before serving.
The pastries can be stored in an airtight container at room temperature for up to 2 days.
The glaze can be made ahead and stored in an airtight container at room temperature for up to 1 week.
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