Butter and flour two 8" or three 6" pans and line with parchment.
Sift the flour, baking powder, baking soda and salt and set aside.
Crack the eggs into a small bowl and whisk.
Pour the buttermilk and vanilla into a liquid measuring cup and stir to combine.
In the bowl of a stand mixer, cream the butter with the paddle on medium speed (#5) until it is light in color, clings to the sides of the bowl, and looks satiny (this should take about 30-45 seconds).
At the same speed, add the sugar in a steady stream. When all of the sugar is added, turn off the machine and scrape the gritty, sandy mixture clinging to the sides into the center of the bowl. Continue to cream at the same speed for 4-5 minutes, or until the mixture is very light in color and fluffy in appearance.
With the mixer still on medium speed, add the eggs a tablespoon at a time. Continue to cream, stopping the mixer and scraping the sides of the bowl at least once. When the mixture is fluffy, white and increased in volume (it should look like whipped cream cheese and the graininess should disappear) take the paddle and bowl off of the mixer.
Add 1/4 of the dry ingredients, sprinkling over the top of the creamed butter. Fold in with a rubber spatula, then add 1/3 of the buttermilk mixture. Repeat, alternating dry and wet ingredients. With each addition, scrape the sides of the bowl and continue mixing until smooth.
Spoon equal amounts of batter into each pan. With a rubber spatula, spread the batter, working from the center outward, creating a slightly raised ridge around the outside rim. (This helps to compensate for the usual raised center in baked cakes.)
Bake for 30-35 minutes, or until the baked surface springs back slightly when touched lightly in the center and the sides begin to contract from the pan.
Cool for 10 minutes before inverting on a cooling rack. Peel off parchment from bottoms and allow to completely cook before proceeding.