Preheat oven to 350°F (175°C). Line a cupcake pan with paper liners.

1. In a medium bowl, whisk together flour, baking powder, and salt.
2. In a large mixing bowl, cream the butter and sugar together until light and fluffy.
3. Beat in the eggs one at a time, then mix in lime zest, lime juice, and vanilla extract.
4. Alternately add the dry ingredients and coconut milk to the butter mixture, mixing until just combined.
5. Fold in shredded coconut.
6. Divide batter evenly among cupcake liners, filling each about 2/3 full.
7. Bake for 18–22 minutes, or until a toothpick inserted into the center comes out clean.
8. Cool cupcakes in the pan for 5 minutes, then transfer to a wire rack to cool completely.
9. To make the frosting: Beat softened butter until creamy. Gradually add powdered sugar and mix until smooth.
10. Stir in lime juice, lime zest, and coconut extract if using.
11. Frost cooled cupcakes using a piping bag or spatula.
12. Garnish with shredded coconut and additional lime zest, if desired.