Preheat your oven to 350°F (175°C) and line a mini cupcake pan with liners.
In a bowl, cream together the softened butter and sugar until light and fluffy.
Add eggs one at a time, mixing well after each addition.
Stir in the vanilla extract.
In another bowl, combine the flour, baking powder, and salt.
Gradually add the dry ingredients to the wet mixture, alternating with milk.
Spoon the batter into the prepared cupcake liners, filling each about two-thirds full.
Bake for 12-15 minutes or until a toothpick comes out clean.
Allow the cupcakes to cool in the pan for 5 minutes, then transfer to a wire rack.
Frost with your favorite icing once completely cool.