Step 1

Preheat oven to 300°F. Stir together flour, sugar, baking powder, salt, and 1 tablespoon of the sprinkles in a medium bowl until combined. Stir in melted butter and 1 1/2 teaspoons of the vanilla. Squeeze mixture together using your fingertips until big and small clumps form (batter will not be smooth). Spread clumped batter in an even layer on a rimmed baking sheet. Bake in preheated oven until firm, about 10 minutes. Let cool completely, about 20 minutes. Set aside.

Step 2

Stir together condensed milk, salt, and remaining 2 teaspoons vanilla in a large bowl; set aside. Beat whipping cream in a separate large bowl with an electric mixer fitted with a whisk attachment on high speed until stiff peaks form, about 2 minutes. Fold whipped cream and remaining 1/3 cup sprinkles into condensed milk mixture. Spoon mixture into a 9- x 5-inch loaf pan. Cover with plastic wrap; freeze until cold, about 2 hours.

Step 3

Stir cake crumbles into cold whipped cream mixture. Cover with plastic wrap; freeze until very firm, about 3 hours. To serve, scoop ice cream into bowls, and garnish with additional sprinkles.