Place a rack in the center of the oven. Preheat the oven to 350F.
Grease and flour either two 8 or 9-inch round cake pans or two 12-count muffin tins. You can line the muffin cups with paper liners in place of greasing. Set aside.
Beat together the butter, oil, sugar, baking powder, and salt together with a mixer until well-combined, about 3 minutes on medium-high.
Scrape down the sides.
Add the eggs and then egg yolks one at a time, and mix until well-combined.
Scrape down the sides.
Stir in half of the flour, then all of the milk, and then the remaining flour, scraping the bowl after each addition.
Divide the batter evenly between the prepared pans.
Bake the cake until just golden brown. For cupcakes - 20-30 minutes. For 8-inch and 9-inch round cake pans 35-45 minutes. The cake should have a few moist crumbs attached when a toothpick is inserted in the center but there shouldn't be wet batter.
For round cake pans, cool completely in the pan, then loosen the edges with a knife and gently remove from the pan.
For cupcakes, let cupcakes to cool in the pans for 5-10 minutes, then remove to a wire rack to cool completely.
Notes
Oil: A neutral oil such as canola oil is best.
Flour: Properly measure the flour by aerating, spooning, and then leveling. Check out this tutorial to make a homemade cake flour substitute.
Milk: Anything from skim to whole milk will work. However, whole milk will give you moister, richer cake.