Preheat the oven to 325°F (163°C). Line two baking sheets with parchment paper.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy, about 3-4 minutes.
Add the key lime zest, key lime juice, and vanilla extract to the butter mixture. 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 until the dough just comes together. Do not overmix.
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 24 cookies).
Place the cookies onto the prepared baking sheets, spacing them about 1 inch apart.
Bake in the preheated oven for 12-15 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.
Transfer the cookies to a wire rack to cool completely.
Once cooled, dust the cookies with powdered sugar if desired before serving.