Preheat the oven to 325°F (163°C). Line two baking sheets with parchment paper.
In a large bowl, cream together the softened unsalted butter and granulated sugar using an electric mixer on medium speed until light and fluffy, about 3 minutes.
Add the key lime zest, fresh key lime juice, and vanilla extract to the butter mixture. Mix until fully incorporated.
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 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 or knife to cut the dough into desired shapes (approximately 2-inch rounds).
Place the cookies about 1 inch apart on the prepared baking sheets.
Bake in the preheated oven for 18 to 20 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.
Transfer the cookies to a wire rack to cool completely.
Once cooled, dust the cookies lightly with powdered sugar before serving.