WET INGREDIENTS: Add 1 cup butter to the base of a stand mixer. Add in 1-1/2 cups white sugar and 3 tbsp lime zest. Beat until creamy, about 2-3 minutes. Scrape sides and add in 2 eggs, 1-1/2 tsp vanilla, and 1-1/2 tsp. coconut extract. Beat until mixed.
DRY INGREDIENTS: Scrape sides and add 2 tsp baking powder and 1 tsp salt. Mix to combine. Finally, add in the 3 cups flour and beat just until combined and no streaks of flour remain.
CHILL: Cover dough tightly and chill in the fridge for 20 minutes. Line a large plate with parchment paper.
FORM COOKIE DOUGH BALLS: Portion out the dough, measuring each ball to be exactly 1/4 cup (60 grams) of dough. (I don't recommend bigger or smaller cookies -- they work best at this size -- Note 5.) Repeat with remaining dough to get about 16-18 total cookie dough balls. Once dough balls are formed, roll each dough ball in the 1/2 cup powdered sugar and then set on the plate.
CHILL AGAIN: Return dough balls to the fridge for 20 minutes or freezer for 10. Meanwhile, preheat the oven to 325 degrees F (162 degrees C). Line a large sheet pan with parchment or a Silpat liner.
BAKE AND COOL: Add cookies to the prepared pan, only 6 at a time (they spread and need a lot of space!) Bake for 10-15 minutes or until cookies have puffed up and aren't gooey or wet looking on top. Bottoms/edges should be ever so slightly browning. Be careful to not overbake as you'll lose out on flavor and texture! Remove from oven and let stand on the sheet pan for 5 mins before removing to a wire cooling rack to fully cool. Do not glaze until completely cooled. Repeat to bake all the cookies or save some for later (See Instruction #8).
GLAZE: Combine 2 tbsp lime juice with 1-1/2 cups powdered sugar, 1 tablespoon heavy cream, and a tiny pinch of salt in a medium-sized bowl. Whisk until smooth. Transfer to a small zip-top bag and seal without air. Cut the tip off the bag and drizzle glaze evenly over all of the cookies. If desired, add a touch of lemon zest to the top. Enjoy at room temperature or chilled.
STORAGE: Instead of freezing baked cookies, freeze the dough! Drop the cookie dough balls on a large sheet pan and freeze until solid. Once solid, transfer the frozen cookie dough balls to an airtight container or bag and freeze for up to 3 months. To bake: You can bake these lemon cookies straight from the freezer. There is no need to thaw, but you may need to add a few extra minutes to the baking time. Bake until the edges are lightly browned, and the center is still soft.The glaze doesn't freeze and thaw well, so I recommend making that fresh.