1Heat oven to 350°F (325°F for dark or nonstick pan). Line 13x9-inch pan with foil so foil extends about 2 inches over sides of pan. Grease bottom only of foil with shortening or cooking spray. Make brownies as directed on box. Cool completely, about 1 hour.
2Place pan of brownies in freezer 30 minutes. Remove brownies from pan by lifting foil; peel foil from sides of brownies. Cut brownies into 24 squares, 6 rows by 4 rows; peel foil from squares.
3For each sandwich, spoon 1/4 cup ice cream on bottom of 1 brownie square. Top with second brownie square, bottom side down; gently press together. Roll sides in sprinkles; place in shallow pan. Freeze until firm, about 30 minutes.
4Wrap each frozen sandwich in plastic wrap. Store in freezer.