Heat oven to 350°F (175°C). Line a 9×13 metal pan with a parchment sling and lightly coat with nonstick spray.
In a large bowl whisk flour, sugar, baking powder, baking soda, and salt.
In a separate bowl whisk butter and oil until smooth, then whisk in egg whites, buttermilk, sour cream, and vanilla.
Pour wet into dry and whisk just until smooth. Fold in sprinkles with a spatula (do not overmix).
Spread batter in pan and smooth. Bake 30 to 35 minutes until the center springs back and a toothpick comes out clean. Cool completely in the pan on a rack.
Beat butter until creamy. Gradually mix in powdered sugar, then add vanilla, salt, and enough milk to reach a soft, spreadable texture.
Spread frosting over cooled cake and add sprinkles. Slice and serve.