Preheat the oven to 350 degrees F (175 degrees C). Grease one 6 1/2-inch cake pan and one 4 1/2-inch cake pan.

Mix cake flour, baking powder, and salt in a bowl.

Cream sugar and butter in a large bowl with an electric mixer. Add eggs, one at a time, mixing well after each addition. Mix in vanilla extract. Add 1/2 of the flour mixture and mix until well combined. Pour in 1/2 of the milk and mix again. Repeat with remaining flour and milk until all ingredients are well combined. Pour batter into the 2 prepared cake pans.

Bake cakes in the preheated oven until a toothpick comes out clean; the smaller cake should take 20 to 25 minutes and the larger cake should take 35 to 40 minutes. Remove from oven and completely cool on a wire rack, about 1 hour.

Line a baking sheet with parchment paper and pour sprinkles on top.

Spread frosting on the sides of the larger cake and immediately roll in sprinkles. Place on a serving platter and spread frosting on top. Frost the sides of the smaller cake, roll in sprinkles, and place on top of the larger cake. Frost the top and decorate with sprinkles.