Preheat your oven to 350 degrees F. Grease and lightly flour three 8-inch round pans.
Combine the buttermilk, eggs, vegetable oil and vanilla in a bowl or large measuring cup and whisk until smooth.
Combine the sugar, cake flour, all-purpose flour, baking powder, baking soda and salt in the bowl of your stand mixer. Whisk to combine the dry ingredients.
Place the mixer bowl on the mixer fitted with the paddle attachment. With the mixer on low, begin adding chunks of softened butter and continue blending until the mixture is sandy and no visible chunks of butter remain. Add 1/4 of the liquid ingredients to the dry ingredients and blend on low to combine. Raise the mixer to medium-high speed and beat for 2 minutes, scraping the bowl and beater halfway through beating. Add half of the remaining liquid ingredients to the bowl, blend on low to combine and then scrape the bowl. Add the remaining liquid ingredients and continue to blend on the lowest speed for 2 minutes.
Divide the batter into the prepared pans and bake until a toothpick inserted into the center of the cakes comes out with a few most crumbs stuck to it, 25 to 30 minutes.
Cool the layers in their pans for 15 minutes, then turn them onto a cooling rack and carefully wrap them in plastic wrap while they cool completely.