PLACE wire rack over sheet of parchment paper. Measure 1/2 cup frosting; spoon 1/4 tsp. onto top of each of 12 cookies. Cover with remaining cookies; press together gently to secure. Spread sides and tops of cookie stacks with remaining frosting (from 1/2 cup measure). Place on rack.
SPOON remaining frosting (from can) into microwaveable bowl. Microwave on HIGH 30 sec.; stir. Cool 2 min. Spoon 1/2 Tbsp. frosting over top of each cookie stack; repeat. Continue to spoon frosting over cookies until all frosting is used.
TOP with sprinkles. Refrigerate 1 hour or until frosting is firm.