Using a stand mixer fitted with the paddle attachment, 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 1 ½ 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.

Position a rack in the center of the oven, and heat the oven to 350 degrees 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 ½ -by-5 ½ -inch rectangles (about the size of an index card).

Brush the top surface of the entire scored rectangle with the egg. Spoon 2 tablespoons of the jam or the brown sugar mixture 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 filling mound, so the pastry sheets adhere to each other.

Use a knife, pizza roller or fluted roller, and following the scored lines, cutting the layered dough into 8 rectangles. Place the rectangles, well spaced, on a baking sheet. If you used a knife or pizza cutter, crimp the edges together with the tines of a fork. Use a toothpick or fork to poke holes in the top of each filled pastry to allow steam to escape.

Bake for 35 to 40 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.

To make the glaze for the jam filled pasties: While the pastries are cooling, in a small bowl, whisk together the confectioners’ sugar, vanilla, and enough water to make a smooth, pourable glaze.

To make the glaze for the brown sugar filled pastries: While the pastries are cooling, in a small bowl, whisk together the confectioners’ sugar, milk, cinnamon and vanilla. And more milk if needed to make a smooth, pourable glaze.

When the pastries have cooled for 30 minutes, drizzle the tops evenly with selected glaze, then sprinkle with the rainbow sprinkles (if using). Let stand for 10 to 15 minutes to allow the glaze to set before serving.