Preheat oven to 325 degrees. Line four 8-inch round baking pans with parchment paper and/or spray well with nonstick cooking spray and set aside. (See notes)
In a large bowl, whisk flour, baking powder, baking soda and salt together to combine. Set aside.
In a liquid measuring cup, stir milk and vanilla together. Set aside.
In a separate large bowl, mix butter, oil and sugar together until combined. Mix in eggs and egg whites, one at a time, until mixture becomes very light and fluffy. Scrape the sides of the bowl and mix again briefly.
Alternate adding in flour mixture with milk mixture, being sure to start and end with flour. Scrape the sides and mix again to ensure a smooth batter. Stir the sprinkles in by hand. Divide evenly between baking pans and smooth the top. Bake 25-30 minutes in the lower 2/3rds of the oven. Cake will be done when a toothpick comes out clean or mostly clean with a few moist crumbs.
Cool 15-20 minutes in cake pans before trying to invert on cooling racks. Cool completely before frosting and decorating.