Preheat the oven to 400°F.
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 and 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.