To prepare the pastry dough, whirl flour, confectioners' sugar, and 1/2 teaspoon salt in a food processor with the blade attachment. Add about half of the butter and whirl until no chunks remain. Add remaining slices and whirl briefly to chop them into pea-sized pieces.
Whisk together the egg yolk and strained ice water. Turn food processor on again and quickly begin drizzling yolk/water mixture through the feed tube, stopping before the dough comes together. Pinch some crumbs together between your fingers; if they don’t stick together, add a bit more water and whirl briefly.
Turn the mixture out onto a large piece of plastic wrap. Use the plastic wrap to help you bring the dough together; fold the edges of the dough toward the center and press down until it holds together, taking care not to overwork the dough. Divide it in half and shape into two flat disks wrapped tightly in plastic. Refrigerate for at least 30 minutes.
Preheat oven to 375º F. Whisk together egg white and a pinch of salt. Set aside.
Remove one of the chilled pastry disks from the refrigerator and, on a floured surface, roll the dough to 1/8-inch thickness. Cut as many 3 1/2 to 3/4-inch circles, as you can. Roll out remaining dough and cut additional circles to make 24 total, re-rolling the scraps as necessary.
Place 12 of the rounds on a parchment-lined baking sheet. Set aside. On the remaining rounds, cut vent holes with a sharp knife or miniature cookie cutters.
Add about 1 tablespoon of jam to the center of each round on the prepared baking sheet. Working one at a time, spread egg wash around the the outer 1/4-inch edge of the pastry dough.
Flatten and spread the jam with your finger tip or the back of a spoon within the circle of egg wash.
Gently place a prepared top over the filling, lining up the edges carefully. Lightly press to the edges together with your fingers and then seal with a fork.
Apply egg wash lightly to the entire surface of each pie and sprinkle generously with coarse sugar.
Bake until golden, about 20 to 25 minutes. Let the pies cool for at least 10 minutes before eating as the jam filling will be quite hot straight from the oven. Serve warm or at room temperature.