Preheat the oven to 350°F.

Cream together the butter, oil, sugar, powdered sugar, lemon zest, lemon juice, and eggs until smooth and well combined.

In a large bowl, whisk together the flour, salt, baking soda and cream of tartar.

Add the dry ingredients to the butter mixture 1 cup at a time, mixing after each addition, until all of the dry ingredients have been incorporated into the dough.

Roll the dough into golf ball sized balls and place them 2 inches apart on a cookie sheet.

Dip the bottom of a glass (about 2 1/2 inches wide) in some granulated sugar and then press down on one of the cookie dough balls until it is about 1/2” thick. This will leave a flat middle section with a rough edge.

Repeat with the rest of the cookie dough balls.

Bake the cookies for 8-10 minutes, or until they are just set. They stay soft, so make sure not to over bake them.

Let them cool for 5-10 minutes on the cookie sheet then move them to a wire rack to cool completely.

To make the frosting, cream together the butter, sour cream, and lemon zest until well combined.

Add the powdered sugar, one cup at a time, mixing well after each addition.

Add 2-3 tablespoons of lemon juice to thin the frosting to your desired consistency (start with 2 tablespoons).

Whip the frosting for one minute, then spread about 1 tablespoon of frosting on each cookie.

Allow it to set, and then store the cookies in an airtight container in the refrigerator for up to one week, or freeze for up to 3 months.