• Preheat the oven to 350°F. Line 2 baking sheets with parchment paper and set aside.
• In the bowl of a stand mixer fitted with the paddle attachment, cream the softened butter, the granulated sugar, and the powdered sugar until smooth and well combined, scraping down the sides of the bowl as needed.
• Add the oil, the egg, the lime juice, and the coconut extract. Mix until fully combined, scraping down the sides of the bowl as needed.
• Add the flour, the baking powder, and the salt. Mix until the dough comes together and no dry streaks remain, scraping down the sides of the bowl often to make sure everything is evenly incorporated.
• Using a large ice cream scoop, portion the dough onto the prepared baking sheets, spacing the cookies apart to allow for spreading.
• Gently flatten each dough ball to about ½-inch thick.
• Bake for 10 to 12 minutes, until the centers are set. Do not let the cookies brown around the edges. The bottoms should be just lightly golden.
• Cool the cookies completely on the baking sheets or transfer them carefully to a wire rack before decorating.

For frosting

• For the frosting, add the softened butter and the powdered sugar to the bowl of a stand mixer fitted with the paddle attachment. Mix on low speed until combined.
• Add the lime juice and the lime zest. Mix on medium speed until the frosting is smooth and fluffy, scraping down the sides of the bowl often.
• Once the cookies are completely cool, spread a thin layer of frosting over each cookie.
• Sprinkle with additional lime zest before serving.