Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, beat the softened butter and granulated sugar together with an electric mixer on medium speed until light and fluffy, about 3 minutes.
Add the finely grated key lime zest and fresh key lime juice to the butter mixture and mix until combined.
In a separate bowl, whisk together the all-purpose flour and salt.
Gradually add the flour mixture to the wet ingredients, mixing on low speed until just combined and a soft dough forms.
Turn the dough out onto a lightly floured surface and gently knead it a few times to bring it together.
Roll the dough out to about 1/4 inch thickness.
Use a cookie cutter to cut out 24 cookies and place them on the prepared baking sheets about 1 inch apart.
Bake the cookies in the preheated oven for 12 to 15 minutes, or until the edges are lightly golden.
Remove the cookies from the oven and allow them to cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.
Once cooled, dust the cookies with powdered sugar before serving.