Preheat oven to 350°F. Prepare three 8-inch round pans with baker's floured spray (or grease and line with parchment rounds).
Mix together all dry ingredients (flour, baking powder, sugar, and salt) in a 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 becomes crumbly.
Pour in eggs and mix on low until just incorporated. Mix in the buttermilk on a low speed. Add in vanilla, and mix at a low speed 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 the prepared cake pans (I find a kitchen scale helpful for this part). This guarantees your layers will bake to be the same height.
Bake for 34-37 minutes (or until a toothpick comes out clean). Allow cake layers to cool for 10-15 minutes on a wire cooling rack before removing from pans, and 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 if needed, 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 before trimming so they don't crumble or break!)