Preheat the oven to 350°F. Line 2 baking sheets with parchment paper.
Combine the butter, oil, granulated sugar, and powdered sugar in a large mixing bowl. Beat on medium speed until creamy and well combined. Stop and scrape the sides of the bowl, then beat again until smooth, about 2–3 minutes.
1 cup (227g) salted butter, 3/4 cup (180ml) vegetable oil, 1 1/4 cups (250g) granulated sugar, 3/4 cup (90g) powdered sugar
Add the lime juice, lime zest, eggs, vanilla, and coconut extract and beat well. Scrape the bottom and sides of the bowl again.
2 teaspoons lime zest, 2 Tablespoons lime juice, 2 large eggs, 1 1/2 Tablespoons pure vanilla extract, 1 teaspoon coconut extract
Add the flour, baking soda, cream of tartar, and salt. Mix on low speed just until combined, but do not overmix.
5 1/2 cups (776g) all-purpose flour, 1/2 teaspoon baking soda, 1/2 teaspoon cream of tartar, 1/2 teaspoon salt
Roll the dough into 16 balls (about 3.2 ounces or 91 g per ball of dough) and arrange on the prepared baking sheets with space between each ball. Spray the bottom of a glass or measuring cup with cooking spray, then dip in granulated sugar. Press down on each cookie while twisting gently, to flatten and create cracks around the edges.
Bake for 10–12 minutes just until the edges of the cookies start to turn slightly golden brown. Do not overbake. Remove and cool completely on wire racks. The cookies will continue to set up as they cool even if they are slightly underbaked.