Lip-Shaped Ice Cream Sandwiches

Evenly spread ice cream or sorbet in a 9-by-13-inch rimmed baking sheet; transfer to freezer and freeze until solid.

In a medium bowl, sift together flour, cocoa powder, baking powder, and salt, and set aside. In the bowl of an electric mixer fitted with the paddle attachment, cream butter, sugar, and vanilla. Add eggs and milk, and mix until combined. Add reserved flour mixture, and mix on low speed until incorporated, scraping the sides of the bowl at least once. Divide dough in half, and shape each half into a flat disk. Wrap each disk in plastic wrap, and chill until firm, about 1 hour.

Preheat the oven to 350 degrees. Roll dough out on a nonstick baking mat, sliding an offset spatula under the dough to release it every few turns of the rolling pin. Roll dough to 1/8 inch thick. Transfer to freezer for 30 minutes.

Cut dough using a 4 1/2-inch lip-shaped cookie cutter. Place lips on a parchment-lined baking sheet. Using a small sharp knife, cut a small lip-shaped opening in the center of half the cookies; these will be the tops of the sandwiches. Transfer to oven and bake until just firm, 12 to 15 minutes. Let cool on baking sheet; transfer to a wire rack.

Remove ice cream from freezer. Using lip-shaped cookie cutter, cut out ice cream and place on underside of one of the bottom cookies. Place a top cookie on top of ice cream, top side facing out. Transfer immediately to freezer to harden; repeat with remaining cookies and ice cream. Serve directly from the freezer. Sandwiches can be kept stored in an airtight container in the freezer for 3 to 4 days.