Adjust oven racks to the medium position and preheat oven to 350℉. Grease 2 9″ cake pans and set aside.
In a large bowl, whisk the flour, baking powder, baking soda, salt, and 1 ½ cups of the sugar together. Set aside.
In a medium bowl, whisk together the butter, vegetable oil, vanilla, buttermilk, and 6 egg yolks. Set aside.
Place 3 egg whites (discard the others, or use them for something healthy like an egg white omelet to offset the sugar bomb we have here) in the bowl of a stand mixer. Add a pinch of cream of tartar. Using the whisk attachment, beat on medium-low for about a minute or until they become frothy. Increase the speed to medium-high until soft peaks form. Increase speed to high and slowly add the remaining ¼ cup sugar and beat until the whites are glossy and stiff peaks form. Transfer to another bowl.
Place the flour mixture into the bowl of the stand mixer and slowly add the butter mixture, mixing over low speed. Scrape down the bowl and then mix on medium-low until smooth and fully mixed.
Remove the bowl from the mixer. Use a rubber spatula to fold in ⅓ of the egg whites, fold in another ⅓, mix, then fold in the remaining ⅓ of the egg whites and gently fold until no white streaks remain.
Divide the batter evenly among two pans and tap the pans on the counter gently to release bubbles.
Bake in the preheated oven for 20-22 minutes or until a toothpick inserted into each pan comes out clean. Allow to cool on a wire rack for 10 minutes, then remove from the pans and allow to cool completely before frosting.
To make the frosting, place 1 cup salted butter, 6 cups powdered sugar, and 2 teaspoons vanilla extract in the bowl of a stand mixer and mix on low until the butter and sugar start together. Add enough milk to reach a frosting-y consistency and beat on high until light and fluffy. Add additional milk if necessary.
To assemble the cake, place four strips of paper on the plate, forming a square. Place one layer on the plate and add a dollop of frosting. Smooth it out, then add the second layer and frost the top. Carefully frost the sides. Smooth it out with a frosting knife or a butter knife. If desired, cover in sprinkles (add about 2 tablespoons at a time and gently press them into the cake. To sprinkle the sides, pour them into your palm and gently press it into the side). Carefully remove the paper strips. Makes 12 servings.