Preheat oven to 350°F (175°C) and line a muffin tin with cupcake liners.
In a large bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the mint extract.
In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the dry ingredients. Mix until just combined.
Fill the cupcake liners about 2/3 full. Bake for 18-20 minutes, or until a toothpick inserted into the center comes out clean. Let cool in the tin for a few minutes before transferring to a wire rack to cool completely.
For the frosting, in a large bowl, beat together the butter and powdered sugar until light and fluffy. Gradually add the milk and salt, beating until smooth. Frost the cooled cupcakes and sprinkle with sea salt.