Cream together the softened unsalted butter and granulated sugar using an electric mixer on medium speed for about 2-3 minutes until light and fluffy.

Add the key lime zest and beat for an additional 30 seconds.

In a separate bowl, whisk together all-purpose flour and salt until well combined.

Gradually incorporate the dry mixture into the creamed butter and sugar mixture.

Shape the dough into a log approximately 12 inches long, wrap in plastic wrap, and freeze for at least 30 minutes.

Preheat your oven to 375°F (190°C) and line two baking sheets with parchment paper.

Once chilled, slice the dough into ¼-inch thick pieces and arrange on the prepared baking sheets.

Bake for 12 minutes until the edges are lightly golden but the centers remain pale.

Transfer cookies to a wire rack to cool completely.

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