Preheat oven to 35Prepare cookie sheets with cooking spray or parchment paper.
In the bowl of a stand mixer, cream the butter and sugars until smooth and fluffy. Add oil, lime juice and zest, and eggs. Mix well.
Add flour, baking soda, cream of tartar, and salt. Mix until combined. Dough will be slightly crumbly.
Using a medium cookie scoop, scoop the dough into balls and roll smooth. Place on baking sheet, about 2 inches apart.
Put about 1/4 c sugar on a small plate. Spray the bottom of a glass with cooking spray and dip into the sugar. Press glass gently onto the center of each cookie, until the cookie edges split.
Bake cookies for 8-9 minutes. Don't over bake! Allow cookies to cool on baking sheet for 5 minutes before removing to wire rack to cool completely.