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 step 3.

Whisk the flour, cornstarch, baking soda, and salt together in a medium bowl. Set aside.

In a large bowl using a hand mixer or a stand mixer fitted with a paddle attachment, beat the butter and 1 cup (200g) granulated sugar together on medium-high speed until creamed, about 3 minutes. (Here’s a helpful tutorial if you need guidance on how to cream butter and sugar.) Add the egg, lime juice, lime zest, and coconut extract and beat on high speed until combined, about 1 minute. Mixture will appear curdled and that’s ok. Scrape down the sides and up the bottom of the bowl. Turn the mixer down to medium speed and beat in the coconut. Add the dry ingredients and beat on low speed until combined. Dough is thick, creamy, and sticky.

Cover and chill the cookie dough in the refrigerator for at least 1.5 hours (and up to 4 days). If chilling for longer than a few hours, allow to sit at room temperature for 15 minutes before rolling and baking because the dough will be quite firm.

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

Pour remaining sugar into a large bowl. Roll cookie dough into balls, about 1 Tablespoon of dough per cookie. Roll each in granulated sugar. Arrange 3 inches apart on the baking sheets.

Bake for 12-13 minutes or until very lightly browned on the sides.

Remove from the oven and allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.

Whisk the glaze ingredients together. If desired, add more confectioners’ sugar to thicken or more juice to thin out. The thicker the glaze, the whiter (and less translucent) it will be. Drizzle on cooled cookies and feel free to garnish each with more shredded coconut and/or lime zest. Icing will set after about 1 hour, so these are convenient to store and transport.

Cookies without glaze stay fresh covered at room temperature for up to 1 week. Cookies with glaze stay fresh covered at room temperature for up to 3 days or in the refrigerator for up to 1 week.