Add granulated sugar and brown sugar to a large bowl or the bowl of a stand mixer fitted with the paddle attachment. Add key lime zest and whisk to combine. Let sit 5 minutes.

Add butter to the lime sugar and cream for 2-3 minutes, or until creamed and fluffy.

Mix in egg, key lime juice, baking soda and salt, then mix in flour until cookie dough forms.

Place remaining ¼ cup granulated sugar in a small bowl. Scoop 1 tablespoon sized cookie dough balls and roll in sugar, then place on a cookie sheet covered with parchment paper or a silicone baking mat. No need to space; we are chilling the dough.

Chill the dough for at least 30 minutes.

Preheat oven to 350°F. Line another cookie sheet then spread cookies at least 2-inches apart. Bake for 11-14 minutes or until they just lose their glossy sheen. Cool before frosting, if using.

To frost: whisk powdered sugar key lime zest, then add key lime juice and 2 teaspoons milk, adding more milk as needed for consistency. Drizzle over cookies and let set (it semi-sets, so hard on top but drippy underneath the top layer of icing). Sprinkle with more zest, if desired.

Store in an airtight container for up to 3 days or freeze for up to 2 months.