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Heat the oven to 350°F.
Sift together the flour, baking powder, and salt. Set aside.
Prepare the pans: Rub the bottoms and sides of the cake pans with a little butter, shortening, or baking spray. Make sure to get into the corners and all the way up the sides. Flour the sides and bottoms of the pan by scooping a bit of flour into the pan, then shaking and tapping to coat the bottom and sides of the pan with flour; dump out the excess. Alternatively, cut out a parchment round and use this to line the bottom.
Beat the butter and sugar until fluffy and light. Cream together for about 3 to 5 minutes on medium spread (see above notes for more information).
Add the eggs one at a time. Beat until the batter is very smooth and creamy-looking. Adding the eggs one at a time gives them a better chance at incorporating into a smooth batter. Be sure they are room temperature so the batter does not appear curdled.
Beat in half the flour, salt, and baking powder. Add the sifted dry ingredients with the mixer running at low speed. Continue to mix until incorporated.
Beat in the milk and vanilla. Alternate adding in the liquids with the dry ingredients so the milk has a chance to be absorbed without needing to overmix the batter. Stream in the milk with the mixer on low until combined.
Beat in the remaining flour mixture until just combined and no more visible flour remains. Stir a few times with a spatula to make sure no more flour remains on the bottom of the bowl.
Divide the batter between cake pans. Use a scale or mechanical ice cream scoop to evenly divide the batter.
Smooth the tops with an offset spatula. Drop the pans against the counter to shake out air bubbles.
Bake for 25 to 30 minutes: When done, the cake should be puffed like a pillow, golden, and pull away from the sides of the pan. When done, a toothpick inserted into the center of the cakes should come out clean.
Cool for 15 minutes in the pan. Run an offset spatula around the cake to make sure it's completely loosened from the sides of the pan.
Flip the rounds out of the pan, remove the parchment lining, and flip right-side up to cool completely.
Once cool, frost and assemble the cake with the buttercream.