Preheat your oven to 350°F (175°C) and line a mini muffin tin with cupcake liners.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, beat the butter and sugar together until light and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk. Begin and end with the dry ingredients. Mix until just combined.
Divide the batter evenly among the cupcake liners, filling each about ⅔ full.
Bake for 12-15 minutes, or until a toothpick inserted into the center comes out clean. Allow to cool in the tin for a few minutes, then transfer to a wire rack to cool completely.