Preheat your oven to 350°F (175°C). This ensures that your cookies will bake evenly.
In a large mixing bowl, combine the room temperature unsalted butter and icing sugar. Using a whisk, beat them together until the mixture is light and fluffy, about 3-4 minutes.
Add the lime zest, lime juice, and vanilla extract to the butter mixture. Mix until everything is well incorporated.
In a separate bowl, whisk together the all-purpose flour, salt, and cornstarch. Make sure there are no lumps and everything is evenly distributed.
Gradually add the dry ingredients to the wet mixture, stirring gently with a rubber spatula until a soft dough forms. Be careful not to overmix.
Using your hands, roll the dough into small balls, about 1 inch in diameter. Place them on a lined baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are set but the centers are still soft. The cookies will firm up as they cool.
Once out of the oven, allow the cookies to cool on the baking sheet for a few minutes before transferring them to a cooling rack. Once completely cooled, dust them with additional icing sugar for a sweet finish.