Preheat oven to 350 F. Grease three 8-inch round cake pans, line with parchment paper, grease parchment and flour pans.

Pulse ½ cup sprinkles in food processor until coarsely ground, 8 to 10 pulses; set aside. Whisk egg whites, milk and vanilla together in a bowl. Using stand mixer fitted paddle, mix flour, sugar, baking powder, and salt on low speed, about 30 seconds. With mixer running, add butter, 1 piece at a time, until incorporated and mixture resembles moist crumbs. Add all but ½ cup egg mixture and mix until just combined. Increase speed to medium-high and beat until light and fluffy, about 1 minute. Add remaining ½ cup egg mixture in slow stream. Scrape down bowl and beat batter on medium-high speed until well combined, about 15 seconds. Stir in ground sprinkles.

Divide batter evenly among prepared pans and smooth tops with rubber spatula. Bake until toothpick inserted in center comes out clean, 21 to 25 minutes, rotating pans halfway through baking. Let cakes cool in pans on wire rack for 10 minutes. Remove cakes from pans, discarding parchment, and let cool completely on rack, about 2 hours.

Using stand mixer fixed with whisk attachment, whip butter, cream, vanilla and salt on medium-low speed until combined. Slowly add sugar and continue to whip until smooth, about 2 minutes. Add in yellow food coloring then increase speed to medium-high and whip frosting until light and fluffy, about 5 minutes.

Place 1 cake round on a plate. Spread ¾ cup frosting evenly over top. Top with second cake round, then spread ¾ cup frosting evenly over top. Top with third round, and then spread remaining frosting evenly over top and sides of cake. Press remaining ¼ cup sprinkles around bottom edges of cake.