Preheat oven to 325 degrees. Line muffin tins with paper liners and set aside.
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 the 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.
Scoop batter into each cup so it's 3/4 full. Bake 18-20 minutes in the lower 2/3rds of the oven. Cupcakes will be done when a toothpick comes out clean or mostly clean with a few moist crumbs.
Cool 15-20 minutes in muffin tins before trying to invert on cooling racks. Cool completely before frosting and decorating.