Preheat the oven to 350°F (177°C) and prepare three 6-inch or two 8-inch cake pans by spraying the sides with baking spray and fitting a parchment paper circle to the bottom of each pan.
In a medium bowl, add the sifted cake flour, baking powder, baking soda and salt. Whisk together and set aside.
In the bowl of your stand mixer fitted with the paddle attachment (or with a handheld mixer and large bowl), beat the butter on high speed until it's creamy, about 2 minutes. Add the vegetable oil and sugar, then continue to mix on medium-high until pale and fluffy, about 2 minutes. Add the eggs and egg yolks one at a time, mixing on low speed for 10-15 seconds after each addition. Scrape down the bowl and paddle, then add the vanilla and sour cream and turn the mixer to high speed for one minute. The batter may look curdled at this point but don't worry – it will come together in the next step!
Turn the mixer off and add the dry ingredients all at once. Mix on low speed until the ingredients just start to combine, then add the milk in a steady stream and continue mixing until incorporated, about 30 seconds. Scrape down the sides and bottom of the bowl and give it a few stirs to make sure there are no lumps (without over-mixing). The batter will be slightly thick, but pourable.
Pour the batter evenly into the prepared cake pans and bake for 28-32 minutes, until a toothpick inserted comes out clean or with just a few moist crumbs. Let the cakes cool in the pan for five minutes before turning them out onto a wire rack for an additional few hours of cooling. Make sure they're entirely room temperature before applying any frosting.