In the bowl of a standing mixer fitted with a paddle attachment, beat the butter with 1 1/2 cups of the sugar until light and fluffy. Beat in the eggs. Add the flour, cream of tartar, baking soda and salt and beat at low speed until a smooth dough forms. Cover the dough with plastic wrap and refrigerate until firm, about 1 hour or overnight.
Preheat the oven to 350°. In a small bowl, mix the remaining 2 tablespoons of sugar with the cinnamon. Scoop the dough into tablespoon-size balls and roll in the cinnamon sugar to coat. Arrange the balls 2 inches apart on cookie sheets and bake for about 20 minutes, or until golden on the bottom. Leave the cookies on the sheets for 2 minutes, then transfer them to a rack to cool.
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