Preheat your oven to 350°F and line a baking sheet with parchment paper.

In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.

Beat in the egg, followed by the key lime zest and juice, mixing until well combined.

In a separate bowl, whisk together the flour, baking soda, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Drop tablespoon-sized balls of dough onto the prepared baking sheet, spacing them about 2 inches apart.

Bake in the preheated oven for 10 minutes, or until the edges are lightly golden.

Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.

For the glaze, whisk together the powdered sugar and key lime juice until smooth. Drizzle over the cooled cookies.