Preheat oven to 350°F (175°C). Line a 12-cup muffin tin with cupcake liners.
In a medium bowl, whisk together flour, baking powder, and salt. Set aside.
In a large bowl, cream butter and sugar until light and fluffy. Add eggs one at a time, mixing well. Stir in lime zest and vanilla extract.
Gradually add dry ingredients to wet ingredients, alternating with lime juice and milk. Mix until just combined.
Divide batter evenly among liners, filling ¾ full. Bake for 18-20 minutes or until a toothpick inserted in the center comes out clean. Cool completely on a wire rack.
Mix condensed milk, lime juice, and lime zest in a bowl until thickened. Hollow out the center of each cupcake and fill with the mixture.
Beat butter until smooth. Gradually add powdered sugar, lime juice, and zest. Frost cupcakes and garnish with lime zest and lime slices.