Preheat the oven to 350F then line a baking sheet with parchement paper and set aside.
Cream the butter, oil, sugar, and powdered sugar in a large mixing bowl or a stand mixer.
Add the egg, lime juice,lime zest, and coconut extract to the sugar butter mixture and mix until combined.
Add the flour, salt, and baking powder and mix until combined, using a large cookie scooper, scoop out 9 equally sized cookie balls and place on a parchement lined baking sheet .
Spray the bottom of a glass or measuring cup with cooking spray, dip into a plate of granulated sugar, and gently press the cookie down. Make sure not to smash the cookies too thin.
Bake for 8 minutes, cool on the baking sheet for 10 minutes before transferring them to a wire rack to cool fully before frosting.