Preheat the oven to 350F degrees and line a muffin pan with muffin papers.
Place the ½ cup shredded coconut in a food processor or blender and process until it's a fine powder.
Then in a medium bowl whisk together the flour, processed coconut, baking powder and salt.
Beat the butter and sugar together in a large bowl using an electric mixer until fluffy. Beat in the eggs, vanilla extract & coconut extract.
Turn the mixer down to low speed and beat in the flour mixture followed by the coconut milk.*
Spoon the batter into the prepared muffin papers and bake for 15-17 minutes or until an inserted toothpick comes out clean.
If you're planning to add toasted coconut as decoration - place ⅓ cup in an even layer on a cookie sheet. Bake in the oven at 325F for 5-10 minutes. Watch closely as it only take about 1 minute for the coconut to go from toasted to burnt.
While the cupcakes are cooling you can get started making the frosting.
In a large bowl beat the butter until very fluffy. Then add in the lime zest and beat in the powdered sugar about 1 cup at a time.
Once combined, beat in the lime juice 1 tablespoon at a time until you get the desired flavor. Finally with the mixer at medium-high speed, beat in the tablespoon of whipping cream (if needed).
Frost the cooled cupcakes using a piping bag & tip (I used a 1M tip) or a knife. Then sprinkle with toasted coconut.