Beat butter and all the sugar on medium speed until well blended. Add eggs and vanilla and beat on high speed until well blended.
Sift together flour, baking powder, and salt.
With mixer on low speed, add one third of the flour mixture, followed by a third of the buttermilk – repeat, alternating in thirds. When all the flour is incorporated beat mixture on medium speed just until well blended.
Fill paper-lined or buttered muffin cups (1/3-cup capacity) about three-fourths full with batter (about 1/4 cup in each).
Bake in a 350° oven until tops spring back when lightly touched in the center, 20 to 25 minutes. Cool on racks 5 minutes; remove from pans. Cool completely.