Shred the cold butter with a box grater, then whisk the flour, sugar, and salt in a large bowl before working in the butter and stirring in the discard and cold water. Look for coarse, sandy crumbs with visible butter pieces before adding the wet ingredients.
Press the mixture together with your hands, incorporating up to an additional ¼ cup cold water only where needed. The dough should hold its shape when squeezed, without loose flour falling away.
Shape two flat disks, enclose each in plastic wrap, and refrigerate for at least 1 hour or up to 3 days. Properly chilled dough feels firm, with no soft, greasy patches.
Heat the oven to 350°F, cover a baking sheet with parchment, and roll one disk on a floured surface to about ⅛ inch thick while keeping the second disk refrigerated. A consistent thickness helps the centers and edges bake evenly.
Cut 3-by-5-inch rectangles, arrange half on the sheet, and place 1 tablespoon jam in each center with a clean ½-inch border before covering with matching rectangles and pressing the edges first with fingers, then a fork. The finished seam should lie flat, with no jam squeezed between the dough layers.
Refrigerate the assembled pastries for 20 minutes, using the freezer instead if preferred for this brief chill. The pastry should firm up again so the butter doesn’t immediately soften and spread in the oven.
Beat the egg with the heavy cream and brush the mixture across the chilled pastry tops. A light, even coating encourages a glossy, golden finish without puddles around the edges.
Bake for 25 to 30 minutes, then leave the pastries to cool completely before icing. Use a golden-brown crust as the baking cue and a completely cool surface as the glazing cue.
Stir the powdered sugar, strawberry jam, and heavy cream into a glaze, spread it over the cooled pastries, and add sprinkles if desired. The icing should cover the tops rather than immediately melting into the crust.