Preheat oven to 350°F (175°C) and line two large baking sheets with parchment paper or silicone mats.
In a large bowl or stand mixer, cream together the softened butter and granulated sugar until light and fluffy, about 2 to 3 minutes.
Add the egg, key lime juice, and key lime zest to the butter mixture and beat until thoroughly combined.
In a separate medium bowl, whisk together the all-purpose flour, salt, baking powder, and baking soda.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined.
Scoop the dough by level tablespoons and roll into 1-inch balls using your hands.
Place the powdered sugar in a small bowl and roll each dough ball in the sugar until thickly coated.
Arrange the coated balls on the prepared baking sheets, spaced 2 inches apart.
Bake for 10 to 12 minutes until the edges are set and the tops have a cracked appearance; do not overbake.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.