Preheat the oven to 350°F (175°C).

In a mixing bowl, combine flour, sugar, baking powder, and salt.

In another bowl, whisk eggs, coconut milk, vanilla extract, and lime zest.

Mix the wet ingredients into the dry ingredients until just combined.

Fold in shredded coconut.

Pour the batter into a muffin tin lined with cupcake liners.

Bake for 20 minutes or until a toothpick comes out clean.

In a mixing bowl, beat the softened butter until creamy.

Gradually add powdered sugar, lime juice, and lime zest, mixing until smooth.

Frost the cooled cupcakes with the lime frosting.