Prepare the dough for:

Divide the dough in half, wrap tightly, and refrigerate for 1 hour.

Preheat the oven to 350°F. Line 2 baking sheets or cookie sheets with parchment paper.

Working with 1 piece of dough at a time, roll out to a ¼-inch thickness and cut out with a 1 ½-inch cutter. Use a small round or heart-shaped cutter to cut out the center of half of the cookies. Gather the scraps and reroll one time to cut out more cookies. Arrange on the baking sheets 1 inch apart and bake until golden, 12 to 15 minutes, switching racks and rotating the sheets halfway through. Let cool for 2 to 3 minutes on the sheets, then transfer to a wire rack to cool completely.

Boil for 2 minutes in a small saucepan:

Cool to lukewarm. Sift over the cookies with the cut-out centers:

Turn the solid cookies over, so the bottom side is facing up. Place a small dollop of preserves on the solid cookies. Place a sugar-dusted cut-out cookie over the jam-topped cookies.