Prepare cake batter and bake as directed on package for 2 (9-inch) round cake layers, blending dry pudding mix and milk into batter before pouring into prepared pans. (Batter will be thick.) Cool cakes 10 min.; remove from pans to wire racks. Cool completely.
Meanwhile, beat cream cheese, butter and vanilla in large bowl with mixer until blended. Gradually beat in sugar. Make chocolate curls from 1 oz. each semi-sweet and white chocolates (see tip); refrigerate until ready to use.
Cut each cake layer horizontally in half. Stack on plate, spreading 3/4 cup cream cheese frosting between each layer. Spread remaining frosting onto top and side of cake.
Microwave COOL WHIP and remaining semi-sweet chocolate in microwaveable bowl on HIGH 1-1/2 min., stirring after 1 min.; stir until chocolate is completely melted and mixture is well blended. Cool 5 min. Pour over cake, letting excess drip down side. Garnish with chocolate curls. Keep refrigerated.