In a large mixing bowl, cream the softened butter and sugar together until the mixture becomes light, smooth, and creamy with no visible lumps.
Add the egg to the mixture and beat well until fully combined. Pour in the key lime juice and add the lime zest. Mix until the batter is smooth and slightly fluffy.
In a separate bowl, combine the flour, baking powder, baking soda, and salt. Stir until evenly mixed.
Gradually add the dry ingredients into the wet mixture. Stir gently until a soft dough forms. The dough should be slightly sticky but hold its shape.
Cover the dough and refrigerate for about 1 hour to firm it up and make it easier to handle.
Scoop small portions of dough and roll them into balls about the size of a tablespoon.
Roll each dough ball in powdered sugar until fully coated with a thick, even layer.
Place the coated dough balls onto a parchment-lined baking sheet, leaving space between each one.
Bake in a preheated oven at 350°F (175°C) for 10 to 12 minutes, until the edges are set and the centers remain soft.
Let the cookies cool on the baking sheet for a few minutes before transferring them to a cooling rack to cool completely.