1. Line a baking sheet with parchment paper; set aside. On a lightly floured surface, roll one disk of dough into a large round, about 1/8 inch thick. Using a 3-inch cookie cutter, cut out 12 rounds. Transfer rounds to prepared baking sheet; refrigerate until chilled, about 30 minutes.

2. Repeat process with the remaining dough, using a 4-inch cookie cutter to make 12 more rounds; do not refrigerate. Remove chilled disks from refrigerator.

3. Using paper towels, blot the poached apricots halves to eliminate excess liquid; place one in center of each chilled round. Brush cold water around edges of dough; cover each with an unchilled round. Gently press edges together to seal. Refrigerate about 30 minutes.

4. Preheat oven to 425 degrees. Remove tarts from refrigerator. Using a paring knife, slash the top of each tart in a crosshatch fashion. Brush with water, and generously sprinkle with sugar.

5. Bake 15 minutes. Reduce oven heat to 350 degrees. Continue baking until golden brown, 15 to 20 minutes more. Transfer pies to a wire rack to cool slightly before serving. Or let cool completely, and store in an airtight container at room temperature up to 4 days.