Step 1

Preheat oven to 350°F. Line 2 (8-inch) square baking pans with parchment paper, allowing 2 to 3 inches to extend over sides; spray parchment paper with cooking spray. Prepare brownie batter according to package directions; stir in vanilla until just combined. Divide batter evenly among prepared pans, and, using a small offset spatula, spread into an even layer. Bake both pans at once, side by side, in preheated oven until a wooden pick inserted in center comes out with a few moist crumbs, 18 to 20 minutes. Let cool in pans on a wire rack 5 minutes. Freeze brownies in pans, uncovered, until completely cool, at least 20 minutes or up to 1 hour.

Step 2

Working quickly, spread ice cream in an even layer over top of 1 cooled brownie pan. Remove brownie from second pan, using excess parchment paper as handles and reserving parchment paper. Place second brownie on ice-cream layer, top side up, pressing gently to seal. Cover with reserved parchment paper. Place empty 8-inch square pan on top of assembled ice-cream sandwich stack to weigh sandwich down. Freeze until firm, about 1 hour. Run knife around edges to loosen ice-cream sandwich stack, and remove from pan to a cutting board, using excess parchment paper as handles. Using a sharp knife, cut into 2 1/2-inch squares. Roll exposed edges of ice cream in sprinkles, if desired. Serve immediately, or store in an airtight container in freezer up to 2 months.