Pulse the coconut shreds in a food processor or chop them up with a sharp knife so they are finer. Smaller pieces make a more desirable texture in the baked cookies. Set aside for next step.

Using a handheld or stand mixer fitted with a paddle attachment, beat the butter for 1 minute on medium speed until completely smooth and creamy. Add the confectioners’ sugar, vanilla extract, coconut extract, and lemon zest and then beat on medium-high speed until combined. Scrape down the sides and up the bottom of the bowl and beat again as needed to combine. Add the lemon juice, salt, coconut, and flour and beat on medium speed until combined. The dough may not come together at first, but keep mixing until it does. The cookie dough will be thick.

Cover the cookie dough tightly and chill in the refrigerator for 30 minutes and up to 3 days. (If chilling for 2+ hours, let the cookie dough sit at room temperature for at least 30 minutes before rolling into balls. The cookie dough will be very stiff after being in the refrigerator that long.)

Preheat oven to 350°F (177°C). Line large baking sheets with parchment paper or silicone baking mats. Set aside.

Roll the cookie dough into balls, about 1 Tablespoon of dough each, and place dough balls 2 inches apart on the baking sheets. If the cookie dough is too crumbly, keep rolling and working it with your hands. The warmth of your hands will help bring it together.

Bake the cookies until lightly browned around the bottom edges, about 14-15 minutes.

Allow the cookies to cool for 5 minutes on the baking sheet and then transfer to a wire rack. Make sure cookies are cool to the touch before dipping in icing.

Whisk all of the glaze ingredients together in a medium bowl. If desired, add more confectioners’ sugar to thicken or more milk to thin out. Dip cookies in icing or drizzle on top. If desired, garnish with coconut, sprinkles, and/or lemon zest. If coated lightly, the icing will set after 2 hours.

Cover leftover iced cookies tightly and store at room temperature for 1 day or in the refrigerator for up to 1 week. Cookies without icing can sit covered at room temperature for up to 1 week.