Stir 1 1/2 cups flour, sugar, and baking powder together in a mixing bowl. Drop in the butter and toss to coat with the flour mixture. Using the tips of your fingers, rub the butter into the flour until the pieces of butter resemble small corn flakes. (Work quickly, to keep the butter as firm as possible.) Beat the egg yolk and 1/4 cup ice water in a separate, small bowl until blended. Drizzle over the flour-butter mixture and toss just until you have a rough dough. Don't overmix. If there are some pieces of unmoistened dough, drizzle more ice water, about 1 teaspoon at a time, over the dough, and toss lightly to mix. Turn out onto a work surface and knead lightly a few times, just to gather the dough into a ball. Wrap the dough tightly in plastic wrap, and refrigerate at least 1 hour or up to 1 day.
Lightly butter a 9 x 13-inch baking sheet.
Preheat the oven to 350°F
Cut off and set aside one-third of the dough. Roll out the remaining two-thirds of the dough on a lightly floured surface to a 10 x 14-inch rectangle. (Don't worry if it's not perfectly shaped--you'll have a chance to patch the dough.) Flour the surface lightly, as necessary to keep the dough from sticking. Transfer the dough to the prepared pan, covering the bottom completely and pressing the dough along the sides. Trim any overhanging dough, and use the pieces to patch any holes and gaps. Spoon the preserves in an even layer over the dough. Roll out the remaining dough to a circle about 10 inches in diameter. Cut the dough into 1/2-inch strips. Form a lattice pattern over the preserves with the strips of dough by arranging half of them diagonally, then laying the second half of the dough strips perpendicular to the first.
Bake until the dough is golden brown, about 25 minutes. Remove, and cool completely before cutting into squares. Crostate can be stored in an airtight container at room temperature for up to 3 days.