Preheat the oven to 350 degrees F. Line 24 muffin cups with paper liners. Whisk 2 2/3 cups flour, 2 teaspoons baking powder and 1 teaspoon salt in a medium bowl.
Beat 2 sticks softened butter in a large bowl with a mixer on medium-high speed until smooth, about 1 minute. Add 2 cups sugar and beat until creamy, about 4 more minutes. Beat in 4 eggs, one at a time, then 4 teaspoons vanilla. Reduce the speed to low and beat in the flour mixture in three batches, alternating with 1 cup milk. Beat on medium-high speed until just combined.
Divide the batter among the muffin cups and bake until the tops spring back, 20 to 25 minutes. Let cool 5 minutes in the pans, then remove the cupcakes to a rack to cool completely.