Preheat the oven to 350°F / 175°C. Generously grease three 8-inch / 20cm cake pans (or a 9 by 13-inch / 24 by 36cm cake pan), then line them with greased parchment paper.

In a stand mixer fitted with the paddle attachment, cream the butter on medium-high speed until creamy and smooth, about 1 minute.

Turn the mixer speed to medium; add the oil, sugar, and vanilla to the butter; and beat for about 5 minutes, until the mixture is light in color and about double in volume.

Turn the speed to medium-low and add the eggs and egg yolks, one at a time, mixing each until incorporated before adding the next. Scrape the bowl after each addition.

In a medium bowl, whisk together the flour, baking powder, and salt until well combined. In a liquid measuring cup, whisk together the milk and sour cream.

Add one-third of the flour mixture to the butter mixture and mix until combined. Scrape the bowl and add half of the milk mixture, mixing until combined. Repeat with another one-third flour, the remaining milk mixture, and then finish with the final one-third flour, scraping the bowl and paddle after each addition.

Pour the batter into the prepared pans and spread evenly using an offset spatula. Gently tap the pans on the counter several times to release excess
air bubbles.

Bake until a tester comes out clean, 25 to 30 min- utes (45 minutes for a sheet cake). Let the cakes cool completely before removing from the pans by inverting onto wire racks.

Remove the parchment paper and place one cake layer on a serving plate.

Using an offset spatula, spread a 1 ⁄4-inch / 6mm-thick layer of the buttercream over the cake, making sure it goes all the way to the edge. Place the next cake over that and top with another layer of buttercream. Repeat with the last cake. If desired, at this point, you could crumb-coat the cake.

Decorate the cake with a smooth layer of the remaining buttercream.

Serve the cake immediately or store at room temperature, covered, for up to 48 hours.