In a large mixing bowl, beat the soft, room-temperature unsalted butter and granulated sugar together using an electric mixer on medium speed for about 2-3 minutes.

Gently fold in the finely grated key lime zest using a spatula or wooden spoon.

In a separate bowl, whisk together the all-purpose flour and salt until well combined. Gradually add this dry mixture to the butter-sugar blend, stirring just until incorporated.

Turn the dough onto a lightly floured surface and shape it into a log approximately 12 inches long and 1.5 inches in diameter. Wrap the log tightly in plastic wrap and place it in the freezer for at least 30 minutes.

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

Remove the dough log from the freezer and gently unwrap it. Slice the log into ¼-inch thick rounds and arrange them on the prepared baking sheets.

Bake in the preheated oven for 12 minutes, rotating the pans halfway through.

Once baked, let the cookies cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely.

Prepare the glaze by whisking together powdered sugar and key lime juice until smooth.

Spread or drizzle the glaze over the top of each cookie and allow it to set for about 15-20 minutes.