Preheat the oven to 350° Fahrenheit. Cover a large baking sheet with parchment paper and set aside.
Blend butter and powdered sugar with an electric mixer at medium speed until the texture is fluffy. Add lime juice and lime zest and combine well.
Sift in flour and cornstarch. Once combined, remove the dough and shape with your hands in a large ball.
Chill for 30 minutes
Cut the dough in half and form little 1-inch dough balls. Place the dough balls onto the baking sheet and bake for 20 minutes.
Place the hot cookies on a cooling rack and dust with powdered sugar.
*If you don't own a stand mixer you can use a hand mixer instead. I have never tried it, but I think you could also use a food processor to blend your ingredients. **Use the flat beater attachment if you are using a KitchenAid stand mixer. If you are wondering if you can make the key lime cookies ahead of time. The answer is YES!As long as you store the cookies in an airtight container, you can store them for up to 2 weeks. If you choose you can also freeze the cookies. If you choose to freeze them, don't sprinkle them with powdered sugar until after you have defrosted them.