Preheat oven to gas 3 / 190C / 325F and line a baking sheet with parchment paper
Mix the flour, sugar, desiccated coconut, lime zest and extract together in a bowl then add the cubed margarine
Rub in the margarine and knead until the dough comes together, adding up to 4 tsp of coconut milk as required. The dough should be smooth and dry - not sticky
Shape dough into a ball, then divide in half. On a lightly floured surface, roll out one of the dough portions to about 1/4-inch thick
Using a 2 inch round cutter, cut out shapes from the dough. Place the cutouts 1 inch apart on the baking sheet. You should get roughly 24 rounds from each dough half
Bake for 15 - 18 minutes, or just until the bottoms start to brown. Transfer cookies to a wire rack and let cool
Mix the glaze ingredients together using just enough coconut milk to form a thick paste and ice the cookies, sprinkling extra zest on top to decorate if you like
They'll keep well in a lidded container for 3 or 4 days
