In a large mixing bowl, cream together butter, shortening, sugar and eggs until smooth.
Mix together flour, cream of tartar, baking soda and salt. Gradually mix in to wet ingredients until completely combined and a sticky dough forms.
Cover and refrigerate dough at least 8 hours or overnight.
Preheat oven to 400°F.
On a floured surface, roll dough to 1/4-inch thickness. Cut dough with cookie cutters or the rim of a glass jar.
Place cookies about 1 inch apart on an ungreased cookie sheet or non-stick baking mat. Bake 6-8 minutes. Cookies will still be pale on the top but golden on the bottom.
Remove to a cooling rack and let cool completely before icing.