Set the oven to preheat at 400 degrees F.
Mix the butter, eggs, shortening, and 1½ cups of the sugar with an electric mixer on medium speed until creamy or about 1 to 2 minutes.
Sift together the flour, cream of tartar, baking soda and salt. Add it into the shortening mixture.
Mix the 2 tablespoons of sugar with the cinnamon in a small bowl or on a small plate.
Roll about a tablespoon of dough (more or less) into 1½-inch balls, and roll them in the cinnamon-sugar. Set them about 2 inches apart on an ungreased cookie sheet.
Bake until the cookie edges set, but the centers are still soft. That should be about 8-10 minutes, depending on your oven. Cool on wire racks.
