Preheat oven to 350 degrees Fahrenheit. Line baking sheets with silicone mats or parchment paper.
Whisk together the flour, baking powder, and salt in a bowl. Set aside.
Using a stand mixer with the paddle attachment, cream the butter, sugar, and shredded coconut until light and fluffy.
Add the eggs, one at a time, mixing well after each addition. Add the key lime zest, juice, and coconut extract. Mix to combine.
On low speed, gradually add the flour mixture, mixing until just combined. The dough will be thick and slightly sticky.
Place powdered sugar in a small bowl. Using a small cookie scoop (#40 scoop; about 1 1/2 – 1 3/4 Tbsp of dough), spoon the cookie dough into a ball and drop it into the powdered sugar. Roll it around until coated completely and place it on the prepared baking sheet. Repeat the process placing cookies about 2 inches apart.
Bake at 350˚F for 9-11 minutes, until cookies are puffy and the edges are firm to the touch. Cool several minutes on the pan, then transfer to a wire rack to cool completely. Store cookies in an airtight container.