1. Preheat oven to 350 degrees. Line 2 standard muffin tins with paper liners. Whisk together flour, baking powder, and salt.
2. With an electric mixer on medium-high speed, beat butter and sugar until pale and fluffy, about 4 minutes. Mix in the eggs, one at a time, scraping down sides of bowl as needed, until well blended. Mix in vanilla.
3. Add flour mixture in three batches, alternating with milk in two batches, beating until combined after each. Divide batter evenly among prepared muffin tins. Bake, rotating tins halfway through, until tops spring back when lightly touched, about 20 minutes. Let cool in tins on wire racks.
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