Preheat the oven to 350°F. Lightly grease and flour three 8-inch cake pans or two 9-inch round cake pans. If desired, line the bottom of the pans with parchment rounds.

In the bowl of a stand mixer fitted with the paddle attachment, combine the flour, sugar, baking powder, salt, and baking soda.

Add the butter and mix on low speed until the mixture looks sandy, about 2 minutes.

Pour in the buttermilk and vanilla extract. Mix on low speed until combined, about 30 seconds. Then increase the speed to medium and continue mixing for 30 seconds.

Add the eggs, one at a time, mixing on low speed until fully combined. Scrape the bottom and sides of the mixing bowl with a spatula after each addition. After adding the last egg, mix on medium-high speed for 30 seconds. The batter should be smooth and thick.

Divide the batter evenly among the pans and smooth the tops with an offset spatula or the back of a spoon. If you have a kitchen scale, each layer should weigh about 15 ounces (425g) for three 8-inch layers, or about 22 1/2 ounces (640g) per layer for two 9-inch layers.

For 8-inch cakes, bake for 21 to 24 minutes. If you’re baking two 9-inch layers, bake for 28 to 33 minutes. The edges should just be starting to pull from the sides of the pan and turning golden brown. A toothpick inserted into the center of one of the layers should come out clean.

Cool the cakes in the pan for 5 minutes. Run an offset spatula or butter knife around the edge of the cakes to loosen them from the pan, then carefully turn them out onto a rack to cool completely.