Preheat your oven to 350°F (175°C) and prepare your baking sheets by lining with parchment paper or silicone mats.

In a large mixing bowl, cream the softened butter and granulated sugar until light and fluffy, about 3-4 minutes.

Mix in the vanilla extract, egg, lime juice, and lime zest until well combined, about 1-2 minutes.

In a separate bowl, whisk together the flour, baking powder, salt, and baking soda. Gradually add to the wet mixture, stirring gently to combine.

Scoop tablespoons of dough and roll into 1-inch balls, placing them on the prepared baking sheets.

Bake for 9-10 minutes or until edges are golden brown; the centers should remain soft.

Let cookies cool on baking sheets for 5 minutes before transferring to a wire rack to cool completely.

Prepare the glaze by mixing powdered sugar, lime juice, lime zest, and vanilla extract until smooth; adjust for consistency.

Glaze the cooled cookies with the mixture and let the glaze set before serving or storing.