Preheat your oven to 325 degrees F. Spray three 8-inch or four 6-inch pans with non-stick spray, line the bottoms with parchment paper and spray again. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, combine the butter, oil, sugar and salt. Beat on medium speed for about 2 minutes, until light and fluffy, and smooth in texture.
Turn the mixer to medium-low and add the eggs and egg yolks, one at a time, scraping down the sides of the bowl in between each addition. Add the vanilla and turn mixer to medium-high and beat for an additional 2 to 3 minutes.
With the mixer on low, alternately add the flour and baking powder with the buttermilk, starting and ending with the flour. Mix until combined.
Mix on low until combined.
Evenly distribute the cake batter in the three pans, about 16 to 17 ounces of batter in each 8-inchpan or 12 ounces in each 6-inch pan. The cake batter will be sticky. Smooth it out with an offset icing spatula or back of a spoon.
Bake the cakes for about 25 to 30 minutes, or until a toothpick inserted in the center of the cakes comes out with only just a few crumbs on it.
Cool the cakes on wire racks for about 10 minutes. Carefully invert the cakes onto cooking racks to cool completely. If you don't plan to stack and decorate the cake right away, level the cakes if needed and then immediately wrap each layer in plastic wrap or tin foil and freeze.
About an hour before assembly, remove the cake layers from the freezer.