Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.

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

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

In another bowl, whisk together the flour, baking powder, 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 for 10-12 minutes or until the edges are lightly golden.

Remove from the oven and let cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.

In a small bowl, whisk together the powdered sugar, key lime juice, and lime zest until smooth.

Drizzle the glaze over the cooled cookies and allow it to set before serving.