Position racks in the top third and center of the oven and heat to 350°F. Line two large cookie sheets with parchment paper.
Place one half of the dough on a well-floured surface and dust the top with flour. Roll out into a ¼-inch-thick sheet, being sure the dough doesn’t stick to the surface (slide a long metal spatula under the dough to check, dusting the work surface and top of the dough with additional flour as needed). Using a 2½-inch round fluted cookie cutter, cut out rounds of dough and place ½inch apart on a cookie sheet. Knead the scraps together, and roll out more cookies until the dough is used up. Repeat the procedure with the other portion of dough. Using a ½-inch round fluted cookie cutter, cut holes from the centers of half the rounds. If the dough softens, making it difficult to cut out the holes, refrigerate it briefly.
Bake, switching the positions of the cookie sheets from top to bottom and front to back halfway through baking, until the cookies are barely beginning to brown on the edges, about 12 minutes. Cool completely on the sheets.
Stir the preserves to loosen them. For each cookie, spoon about 1teaspoon of preserves into the center of an uncut cookie round and top with a ring-shaped round. Sift confectioners’ sugar over the cookies.