Preheat the oven to 350°F. Whisk together the flour, salt, and baking soda in a small bowl and set aside.

In a separate mixing bowl, combine the butter, brown sugar, and sugar. Beat with an electric mixer on high for about 1-2 minutes until light and fluffy.

Add the egg and vanilla extract, beating until mixed in. Add the key lime zest, then 1/3 of the flour mixture, mixing only until integrated.

Gradually continue adding the flour mixture until a dough forms.

Roll the dough into 1 ½ inch balls and arrange them on a parchment-lined cookie sheet. Bake for about 8-10 minutes.

Allow the cookies to cool on the sheet for 2-3 minutes before transferring to a cooling rack.

Once completely cooled, whisk together the glaze ingredients, adjusting the liquid or powdered sugar to reach your desired thickness.

Allow the glaze to sit for several minutes before dipping cookies into it or spreading over the top with a knife.

Let the icing set before serving. Store any remaining cookies in an airtight container for 4-5 days.