Whisk together the egg whites and ¼ cup of the milk in a small bowl until slightly combined. Set aside.
In a mixing bowl, beat butter, sugar, and vanilla for 2 minutes on medium speed, scraping down the sides of the bowl as needed. Add in dry ingredients and mix until combined. Beat in egg white mixture until fully blended. Add in remaining milk and beat for 3-4 minutes, scraping down the sides of the bowl. Fold in sprinkles.
Spray two 9inch cake pans with baking spray. Pour batter into pans and bake in a 350 degree oven for 26-28 minutes. Remove and cool completely on wire rack.
For the frosting:
Beat butter for 3 minutes using whisk attachment on an electric mixer. Add in powdered sugar, heavy cream and vanilla. Beat an additional 4-5 minutes, scraping down the sides of the bowl as needed.
To assemble, place one layer of cake on a cake stand. Add a large amount of frosting to top and smooth with an offset spatula. Top with second layer of cake. Apply frosting to entire cake. To add the sprinkles to sides of cake, place cake on a baking sheet (to help catch excess sprinkles). Fill hand with sprinkles and press gently into sides of cake. Repeat until desired amount of sprinkles are applied.