First add the butter, ½ cup sugar, and lime zest to a bowl and cream together until light and fluffy, about 2 minutes. Then, add in the lime juice, dried coconut, coconut extract, and ground flaxseed and mix together for another 30 seconds.
Next, add the sifted flour, baking powder, and baking soda to the mixing bowl. Make sure to add the flour first and then mix the baking powder and baking soda into the flour before mixing. Then, mix together until a smooth and thick cookie batter forms. Do not overmix or else you will form too much gluten and the cookies will not spread as much and be tough.
Add the bowl of cookie dough to the fridge, cover, and let chill for 30 minutes- 1 hour.
Cover a baking sheet in parchment paper and preheat the oven to 350F. Next, remove the dough from the fridge and use a large cookie scoop to form 8 large cookies. Roll into balls between your palms and then roll each cookie dough ball in a small bowl containing the 2 Tbsp of sugar that was set aside.
Place the coconut lime sugar cookie dough balls onto the baking sheet. If you want flatter cookies, you can lightly press the dough down with your palm, but this is optional. Make sure that each cookie is kept about 2 inches apart since they will spread while baking.
Bake for 14-16 minutes until bottoms are lightly browned and the cookie is cooked through but has slightly soft centers. The cookies will continue baking after they are removed from the oven so the centers should still be soft, but not glossy or raw, when they are removed from the oven. If you would like to make smaller cookies (about 10 vs 6) make sure to adjust the baking time to 11-13 minutes.
Remove the cookie tray from the oven and immediately tap the tray on the counter to produce a more “wrinkly” cookie. Then, let the cookies cool on the baking sheet for 5-10 minutes. The cookies will be soft and puffy out of the oven and will naturally deflate a little while cooling.
While the cookies are cooling, make the coconut lime glaze by mixing the coconut milk and lime juice in a small bowl. Then, gradually add in the powdered sugar and whisk together until a thick glaze forms. Drizzle the glaze on completely cooled cookies and top with optional lime zest. Let sit 5 minutes so the icing can harden and then serve!