Pre-heat oven to 350°

Place 2 tablespoons of sugar in a bowl that a flat bottomed glass will fit into. Set aside.

Blend butter, coconut oil, sugar and powdered sugar with an electric mixture until butter lightens in color.

Add lime zest, juice and egg. Blend to combine.

Add flour, baking soda, cream of tartar and salt and blend to combine.

Use a three tablespoon cookie scoop-to make 15 cookie dough balls. Roll to smooth dough.

Cover a large baking sheet with parchment paper.

Place six cookie dough balls onto the baking sheet. Dip the bottom of the glass into the bowl of sugar and press down and wiggle the glass to flatten the cookie dough to 1/2 to 1/4 inch thickness.

Bake at 350° for 8-9 minutes. Do not over bake. You want the bottoms to me very light.

Remove from the oven and allow 2-3 minutes to cool on the baking sheet.

Then, place cookies on a cooling rack to finish cooling. Repeat with the remaining cookie dough.

With an electric mixer, cream softened cream cheese and softened butter together. Then, add the remaining frosting ingredients and blend until smooth and creamy. 

Frost completely cooled cookies and top with a lime wedge, if desired.

Refrigerate to chill and serve.