Heat oven to 350 degrees F. Spray two 9-inch round cake pans with nonstick cooking spray; line the bottoms with parchment or waxed paper rounds. Spray the paper rounds, dust the pans with flour, and invert pans and tap to remove excess flour. Set aside.
In a medium bowl, combine milk, egg whites, and vanilla. Whisk together until well blended.
In the bowl of a stand mixer, combine cake flour, sugar, baking powder, and salt. Mix on low with the beater blade. Add the butter and continue beating at slow speed until mixture resembles moist crumbs. Add all but 1/2 cup of milk mixture to crumbs and beat at medium speed 1 1/2 minutes. Add remaining 1/2 cup of milk mixture and beat 30 seconds more. Stop mixer and scrape sides of bowl. Return mixer to medium speed and beat 20 seconds longer. Fold in the sprinkles.
Divide batter evenly between the two prepared cake pans. Smooth the tops with a rubber spatula. Place the pans in the preheated oven on the middle rack. Bake for 23-25 minutes or until a toothpick inserted in the center comes out clean. Let cakes rest in pans for 3-5 minutes. Loosen the cake from the sides of the pans with a knife and invert onto wire cooling racks. Let cakes cool completely.
While the cakes are cooling, make the frosting. In the bowl of a stand mixer, add the softened butter. With the beater blade, cream the butter until smooth, using the beater blade. This will take about 3 minutes on medium speed. Add confectioner's sugar, ½ a cup at a time. Add vanilla and a pinch of salt and combine until well-incorporated. Add heavy cream or milk until the frosting has reached the preferred consistency. For a thicker frosting, you can add more confectioner's sugar, a ¼ cup at a time. For a thinner frosting, you can add more heavy cream or milk, 1 tablespoon at time.
Using a serrated knife, trim a very thin layer from the top of each cake, just enough to even out the surface; set scraps aside. Place one cake on a cake stand or plate. Evenly spread vanilla buttercream over the top of the cake. Decorate with sprinkles. Carefully place the second cake on top, cut-side down, so you have a really smooth, even surface to frost. Frost the top and sides of the cake with remaining vanilla buttercream, using an offset spatula or thin knife. Decorate the top with more sprinkles. Cut into pieces and serve!
Note-The cake layers can be made in advance. Bake, cool, and cover tightly with plastic wrap the day before. Store at room temperature. You can also make the frosting the day before. Store in an airtight container in the refrigerator. Let come to room temperature and beat again. Assemble the cake right before you are ready to serve. You can also keep the cake covered with plastic wrap on the counter for up to 2 days. It is best the day it is made though!