Heat the oven to 350 degrees F and oil a 12-hole muffin pan.
In a medium bowl, whisk together the flour, baking powder, and 1/4 teaspoon salt.
Using an electric mixer, beat the butter and sugar in a large bowl until light and fluffy, about 3 minutes. Reduce the mixer speed to medium and add the eggs, one at a time, beating each until incorporated before adding the next. Beat in the vanilla.
Reduce the mixer speed to low and add the flour mixture in three parts, alternating with the milk and beating just until incorporated.
Divide the batter between the muffin holes (about 1/4 cup per hole) and bake until a wooden pick, inserted into the center comes out clean, 18 to 20 minutes. Transfer to a wire rack to cool.