1. Heat oven to 350 degrees F. Line indents of two 12-cup mini cupcake pans with paper or foil liners.
2. Cupcakes. In a medium bowl, combine flour, baking powder and salt. In a second medium-size bowl, combine butter and sugar. Beat with an electric mixer on medium-high for 1 minute. Add egg and beat until combined. On low, beat in half the flour mixture, then the Key lime juice, followed by remaining flour mixture.
3. Spoon evenly into prepared liners. Bake at 350 degrees F for 17 minutes. Cool in pans on wire racks.
4. Frosting. In a small bowl, combine confectioners' sugar, butter and Key lime juice. Beat until smooth. Spread frosting onto cooled cupcakes.