Preheat oven to 325ºF.
In a food processor combine sugar, coconut, 2 Tbsp lime zest and vanilla. Cover and process until finely chopped. Add flour; cover and pulse until just combined. Add butter; cover and process until dough just starts to come
together. Form mixture into a ball and knead with your hands until smooth.
Divide dough in half.
On a lightly floured surface, roll first half of the dough until 1/4 inch thick. Using cookie cutters, cut dough into desired shape. Place on parchment-lined baking sheet 1-inch apart.
Bake for 15-17 minutes until just golden on the bottom. Repeat, re-rolling remaining bits of dough until all is used. Cool for 2 minutes and then transfer to wire racks to cool completely. When cold, frost or drizzle with Lime Glaze.