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

In a small bowl, whisk together flour, baking soda, and salt. Set aside.

In a large bowl, beat butter, granulated sugar, and brown sugar until light and fluffy, about 1–2 minutes.

Add the egg and vanilla extract and mix until combined.

Stir in the key lime zest.

Gradually add the dry ingredients, mixing just until a soft dough forms.

Roll dough into 1½-inch balls and place on the prepared baking sheet.

Bake for 8–10 minutes, until the edges are set but centers are soft.

Cool on the baking sheet for 2–3 minutes, then transfer to a wire rack to cool completely.

Whisk together all glaze ingredients until smooth. Adjust consistency if needed.

Once cookies are fully cooled, dip or spread glaze over the tops. Allow glaze to set before serving.