01 - Whisk together all-purpose flour, baking powder, baking soda, and salt in a medium mixing bowl. Set aside.
02 - In a large mixing bowl, beat unsalted butter and granulated sugar with an electric mixer until light and fluffy, approximately 2 minutes.
03 - Add eggs, one at a time, beating thoroughly after each addition. Blend in vanilla extract, key lime zest, and key lime juice until well combined.
04 - Gradually incorporate the dry ingredients into the wet ingredients, mixing until just combined and no dry spots remain.
05 - Fold in sweetened shredded coconut evenly throughout the dough.
06 - Cover the bowl and refrigerate the dough for at least 30 minutes to allow flavors to develop and dough to firm.
07 - Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
08 - Scoop tablespoon-sized portions of dough. Roll each into a ball, then coat generously with powdered sugar.
09 - Place dough balls 2 inches apart on prepared baking sheets. Bake for 10 to 12 minutes, until edges are set and the tops show a crinkled appearance.
10 - Cool on baking sheets for 5 minutes before transferring cookies to a wire rack to cool completely.