Swig Sugar Cookies {Copycat Recipe}

Name: Swig Sugar Cookies {Copycat Recipe}
Prep time: 1 h
Cook time: 12 min
Total time: 1 h 12 min
Cuisine: American, Southern
Ingredients: 1 cup salted butter (softened); 3/4 cup neutral-flavored oil (canola, vegetable, grapeseed, etc); 1 1/4 cups granulated sugar; 3/4 cup powdered sugar; 1/2 teaspoon baking soda; 1/2 teaspoon cream of tartar; 1/2 teaspoon salt; 2 tablespoons sour cream; 2 large eggs; 1 teaspoon vanilla extract (see note); 5 1/2 cups all-purpose flour (I use unbleached); Granulated sugar for pressing the cookies; 3/4 cup salted butter (softened); 1 teaspoon vanilla extract; 6 cups powdered sugar; 1-2 tablespoons cream or milk