1. Preheat oven to 325°F.
2. In a food processor, combine coconut, sugar, lime zest, and the vanilla extract. Pulse a few times until the coconut is finely chopped. Add flour, and pulse until combined. Gradually add in the butter pieces and pulse until the mixture is smooth and combined. (The dough will appear fairly dry.)
3. Transfer to a very large bowl, and knead dough until smooth. (If the dough is still too dry and crumbly, add in a half teaspoon of water at a time until it clings together.) Shape dough into a ball, then divide in half.
4. On a lightly floured surface, roll out one of the dough portions to about 1/4-inch thickness. Using your desired cookie cutters (I used a 1.5-inch round cutter), cut out dough. Place cutouts 1″ apart on an ungreased cookie sheet.
5. Repeat with the remaining dough on a second cookie sheet.
6. Bake for 15-17 minutes, or just until bottoms start to brown. Transfer cookies to a wire rack, and let cool to room temperature.
7. Drizzle each cookie with the lime glaze, adding extra lime zest on top if desired.

TO MAKE LIME GLAZE:

1. In a small bowl, whisk together powdered sugar, lime peel, and lime juice until combined. Add in the two or three tablespoons of water, and whisk until it reaches a good consistency for spreading.