Preheat the oven to 350°F (175°C) and line a muffin tin with cupcake liners.
Whisk together the dry ingredients in a medium bowl.
Beat butter and sugar until fluffy, then add eggs, lime juice, and zest.
Gradually add dry ingredients alternating with coconut milk. Mix until combined.
Fold in shredded coconut.
Spoon batter into cupcake liners, filling 2/3 full.
Bake for 18-20 minutes, then cool completely.
For frosting, beat butter, add powdered sugar, then lime juice, zest, and coconut milk. Frost cupcakes and garnish with shredded coconut.