NOTE: It is SUPER IMPORTANT that all the room temperature ingredients listed above are room temperature and not cold so that the ingredients mix and incorporate correctly.
Heat oven to 335º F/168º C — 350º F/177º C. I tend to use lower setting to prevent my cakes from getting too dark on the outside before the inside is done baking. Prepare your cake pans with cake goop or another preferred pan release.
Whisk together the eggs, egg yolk, milk, vanilla and vegetable oil together and set aside
Place the flour, sugar, baking powder, baking soda and salt into the bowl of your stand mixer with the paddle attachment.
Attach the paddle to the mixer, and turn on the slowest speed (setting 1 on Kitchen Aid mixers). Slowly add chunks of your softened butter until it is all added. Let mix until batter resembles coarse sand.
Add 1/3 of your egg/milk mixture to the flour mixture while mixing on low until just moistened. This part is crucial. Don't add too much liquid.
Increase mixing speed to medium (setting 5 on Kitchen Aid mixer). Let the mixture whip up until it has thickened and lightened in color (2 minutes of mixing). It should look like soft-serve ice cream. If you do not let the batter mix fully, you will end up with very short, crumbly cakes.
Scrape the bowl. This is an important step. If you skip it, you will have hard lumps of flour and unmixed ingredients in your batter. If you do it later, they will not mix in fully.
While mixing on low, slowly add in the rest of your liquid ingredients, stopping to scrape the bowl one more time halfway through.
Divide your batter evenly between your pans
Bake for 30 minutes and then check your cakes. If they are still jiggly in the center bake for another 5-8 minutes. If they are almost set, bake for another 5 minute or until the center springs back when you touch it.
Let your cakes cool in the pan for 15 minutes or until the pan is just barely warm. Turn them out onto a cooling rack to cool the rest of the way. I like to put mine into the freezer (unwrapped and on the cooling rack to flash chill for one hour so I can begin frosting)
Once my cakes are cold, I fill them with the buttercream and give them a crumb coat. Chill the cake for 20 minutes to set the crumb coat then apply your final coat of buttercream. I decorated my cake with a 1M piping tip and piping bag.