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Preheat the oven to 350 degrees. Grease and line 3 9-inch cake pans with parchment paper.
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Sift together the cake flour, baking powder, baking soda, and salt over a large bowl and set aside.
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In the bowl of a stand mixer fitted with the paddle attachment, beat the butter until smooth. Add 1 ¼ cup of the sugar and beat until smooth and creamy, about 3-5 minutes. Add the egg yolks one at a time until combined. Add the vanilla extract until combined. With the mixer on low, slowly add the flour mixture and buttermilk a little at a time starting and ending with the flour mixture.
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In a separate bowl, beat the egg whites and ¼ cup sugar until soft peaks form, about 3 minutes. Gently fold in the egg whites and rainbow sprinkles until combined. Evenly pour the batter into the 3 cake pans.
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Bake for 30-35 minutes until a toothpick comes out clean. When done, remove the cake pans from the oven and let sit for 15 minutes. Turn the cakes out on a cooling rack and let cool completely before icing.
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For the frosting, beat the butter until smooth. Add the confectioner’s sugar, vanilla extract, and heavy cream and beat until creamy, about 1 minute.