Preheat your oven to 325 degrees Fahrenheit and grease and flour two 9-inch round cake pans (with high sides) or three 8-inch round cake pans (with high sides), lining the bottoms with parchment paper rounds for easy release.
In the bowl of your stand mixer (or in a large bowl using a hand mixer) whip the butter on medium high speed until very smooth. Add the sugar and mix on high speed until fluffy and creamy. The sugar will start to dissolve into the butter a little bit during this creaming process, so you should be able to feel the grains of sugar getting smaller.
Add the eggs and egg yolks one at a time, mixing well after each addition. Scrape down the sides of the bowl regularly at this stage to make sure everything is mixed well.
Mix in the oil and almond extract on low speed.
Measure the buttermilk into a liquid measuring cup and and set aside.
Measure and sift the flour, baking powder, baking soda and salt into a separate bowl and combine with a wire whisk.
Add the dry ingredients and the buttermilk alternatively while the mixer is running on low speed. Add 1/3 of the dry ingredients, half the buttermilk, another 1/3 of the dry ingredients, the other half of the milk, and the remaining dry ingredients.
Turn the speed of the mixer to medium-low and mix until the batter is smooth (about one minute).
Pour the batter into the prepared cake pans and bake at 325 degrees Fahrenheit for about 29-34 minutes, or until a toothpick inserted into the middle of one of the cakes comes out clean.
Cool the cakes in the pans for about 5-7 minutes and then turn them out onto cooling racks to cool completely.
Once the cakes are cool, store them wrapped in plastic wrap in the fridge until ready to frost. They should be refrigerated for at least 1 hour before frosting.