Preheat oven to 350°F (175°C) and line a standard 12-cup muffin tin with paper liners.
In a large mixing bowl, cream together 0.5 cup softened butter and granulated sugar until the mixture is light and fluffy.
Add the egg and 2 teaspoons of vanilla extract, beating until fully incorporated.
In a medium bowl, whisk together the flour, baking powder, and salt.
Add the dry ingredients to the wet ingredients in three parts, alternating with the milk, mixing on low speed until just combined.
Distribute the batter evenly into the prepared cupcake liners, filling each approximately two-thirds full.
Bake for 18 to 22 minutes, or until a toothpick inserted into the center of a cupcake comes out clean.
Allow cupcakes to cool in the tin for 5 minutes before transferring to a wire rack to cool completely.
Prepare frosting by beating 0.5 cup softened butter, powdered sugar, 1 tablespoon milk, and 1 teaspoon vanilla until smooth and aerated.
Apply frosting to the cooled cupcakes using a piping bag or spatula.