Preheat the oven to 350°F (175°C). Line a cupcake tin with paper liners.
In a mixing bowl, cream together the butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition. Stir in the lemon zest and vanilla extract.
In another bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, alternating with the milk. Mix until just combined.
Divide the batter evenly among the cupcake liners, filling each about ⅔ full.
Bake for 18-20 minutes, or until a toothpick inserted into the center comes out clean. Allow to cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.