Preheat oven to 350°F. Prepare three 8-inch cake pans and three 6-inch round pans with baker's floured cooking spray, or grease and line with parchment rounds.
Mix together all dry ingredients (flour, sugar, baking powder, and salt) in a mixing bowl (or stand mixer with a paddle) until fully combined. Mix chunks of room-temperature butter slowly into the dry mix, on a low speed. Continue to mix until no large chunks of butter remain, and the mixture looks crumbly.
Pour in eggs and mix on low until just incorporated. Mix in the buttermilk in two parts, on a low speed. Add in vanilla and oil, and mix on low until fully incorporated. Scrape down the sides of the bowl with a spatula, then beat on medium speed for about 30 seconds.
Divide batter evenly between prepared pans. (I recommend using a measuring cup or kitchen scale to keep the batter amounts even. I added 650 grams of batter to my 8” pans, and 325-350 grams in each of my smaller pans. Measuring the batter guarantees your layers will bake to be the same height.)
Bake for 34-37 minutes, (or until toothpicks comes out clean). Allow cake layers to cool for 10-15 minutes on a wire cooling rack before removing from pans.
Regardless of what cake flavors / sizes you make - cool *completely* before frosting. Set in the fridge or freezer to accelerate the cooling process if desired. (This is a great time to make your frosting.)
Once the layers have fully cooled, they can be leveled and any caramelized bits can be trimmed from the sides / top of the cake using a serrated knife if desired. (Be sure the layers are completely cooled / chilled first; if cut while still warm they tend to crumble or break.)