In a large bowl, combine the butter, shortening, 1 1/2 cups sugar and the eggs and mix thoroughly with an electric mixer on medium speed until creamy and well combined, 1 to 2 minutes. Sift together the flour, cream of tartar, baking soda and salt, and stir into the shortening mixture.
In a small bowl, stir together the remaining 2 tablespoons sugar with the cinnamon.
Shape the dough into 1 1/2-inch balls (1 tablespoon per ball), and roll each ball in the cinnamon-sugar. Arrange the dough balls 2 inches apart on ungreased cookie sheets. Bake two sheets at a time until the edges of the cookies are set but the centers are still soft, 8 to 10 minutes, rotating the sheets halfway through. Transfer the cookies to wire racks for cooling. Repeat with the remaining dough balls. Store in an airtight container.
Recipe adapted from Georgia Cooking in an Oklahoma Kitchen by Trisha Yearwood (c) Clarkson Potter 2008