Preheat your oven to 350°F (175°C). Grease and flour your 8-inch round cake pans.
In a medium bowl, whisk together the cake flour, baking powder, and salt. Set aside.
In a large mixing bowl, cream together the unsalted butter and granulated sugar until light and fluffy, about 3-4 minutes.
Add in the large egg, egg white, and vegetable oil. Beat until fully incorporated, then mix in the vanilla extract.
Gradually add the dry ingredients to the wet mixture, alternating with the whole milk, starting and ending with the dry ingredients. Mix until just combined.
Gently fold in the assorted brightly colored sprinkles, being careful not to overmix.
Divide the batter evenly between the prepared cake pans. Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cakes to cool in the pans for 10 minutes before transferring them to a cooling rack.
Prepare the frosting by beating together the unsalted butter and cream cheese until smooth. Gradually add in the powdered sugar and vanilla extract. Adjust with whole milk if needed.
Once the cakes are completely cooled, place one layer on a serving plate, spread frosting on top, then place the second layer on top. Frost the top and sides of the cake.
Generously sprinkle more bright sprinkles on top and optionally on the sides for an extra festive touch.