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To make the cake: Preheat the oven to 350ºF. Grease and line the bottoms of three 8-inch cake pans or line 24 cups of two muffin tins.
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In a medium bowl, whisk together the flour, cornstarch, salt, and baking powder.
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In a stand mixer fitted with the paddle attachment, cream together the butter and sugar until light and fluffy, 3 to 4 minutes. Add the egg whites, one at a time, mixing well after each addition. Add the oil and the extracts.
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With the mixer running on low speed, add the dry mixture and the milk in two or three alternating batches and mix until just barely combined. Using a rubber spatula, gently fold in the sprinkles until they’re evenly distributed. Distribute the batter among the cake pans or muffin cups, spreading it out evenly if using cake pans.
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Bake until a toothpick inserted into the center comes out clean. Begin checking for doneness at 25 minutes for cakes and 20 minutes for cupcakes.
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Let cool in the pans for 10 minutes and then turn onto a wire rack to cool completely.
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To make the frosting: In a standing mixer fitted with a paddle attachment, beat the butter until smooth and gradually beat in the powdered sugar. Add the salt, extracts, and milk and beat to combine.
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Frost the cake or cupcakes as desired and enjoy.