Preheat oven to 350°. Line bottoms of 4 greased 6-in. round baking pans with parchment; grease paper. In a large bowl, cream butter, oil and sugar until light and fluffy, 5-7 minutes. Add eggs, then egg whites, 1 at a time, beating well after each addition. Beat in vanilla. In another bowl, whisk flour, baking powder and salt; add to creamed mixture alternately with buttermilk, beating well after each addition. Fold in sprinkles.
Transfer to prepared pans. Bake until a toothpick inserted in center comes out clean, 15-20 minutes. Cool in pans 10 minutes before removing to wire racks to cool completely.
For buttercream, in a large bowl, beat butter until creamy. Gradually beat in confectioners’ sugar until smooth. Add cream and vanilla. Beat until light and fluffy, 5-7 minutes.
For drip, in a microwave, heat cream just to a boil. Pour over baking chips; stir with a whisk until smooth. Tint as desired with food coloring. Cool slightly, stirring occasionally.
To assemble cake, place 1 cake layer on a serving plate; spread with ½ cup frosting. Repeat layers. Top with remaining cake layer. Frost top and sides of cake with ½ cup frosting. Freeze until set, about 10 minutes. Frost top and sides with 1 cup frosting. Pour drip over top of cake, allowing some to flow over sides. Pipe remaining frosting around top edges; top with additional sprinkles. Gently press additional sprinkles into frosting on sides of cake.