Preheat the oven to 350 degrees. Line a baking sheet with parchment paper.
Combine the flour, baking powder, and salt together in a bowl; whisk well.
Combine the sugar with the lime zest in a small dish; mix with your fingers until the sugar is fragrant.
Beat the butter with the sugar until creamy. Add the egg and coconut extract. Beat until creamy.
Gradually mix the flour mixture into the egg mixture until combined.
Drop tablespoon-sized balls on the cookie sheet a few inches apart. Flatten them slightly with the palm of the hand.
Place into the oven and bake for 8-10 minutes, or until set and slightly golden brown. Remove from the oven and allow the cookies to cool for a few minutes on the baking sheet before moving them to cool completely on wire racks.
Make the lime glaze by combining the powdered sugar, lime juice, and lime zest together until creamy and smooth.
Once the cookies have cooled completely, place the rack of cookies over parchment paper and spoon frosting on top of each cookie, to taste. Sprinkle a bit more lime zest on top of each cookie, if desired. Let cookies sit until the icing has set. Enjoy!