Preheat the oven to 325 degrees.
Line 2 cupcake pans with paper liners – for a total of 24 cupcakes.
In a medium bowl, combine the sugar and lime zest and mix together with your fingertips until the sugar is moistened and fragrant.
In the bowl of an stand mixer fitted with the paddle attachment, or in a large bowl with an electric mixer, cream the butter and sugar on high speed until light and fluffy, about 5 minutes.
With the mixer on low speed, add the eggs, 1 at a time, taking care to scrape the bowl.
Add the vanilla and mix until well combined.
Meanwhile, in a separate bowl, sift together the flour, baking powder, baking soda, and salt.
Add the dry ingredients in three batches, alternating with the buttermilk, beginning and ending with the dry.
Mix until just combined. Fold in half of the shredded coconut.
Fill each prepared cupcake liner to the top with batter.
Bake for 25 to 35 minutes, until the tops are brown and a toothpick comes out clean. Cool the cupcakes in the pan for 15 minutes, then remove them to a baking rack to cool completely.
Meanwhile, fill a pastry bag fitted with a medium sized round tip with homemade lime curd.
Gently insert the pastry tip into the center of each cupcake and fill with a small amount of lime curd.
Frost each cupcake with Cream Cheese Frosting with Lime and garnish with toasted coconut.