Pumpkin Snickerdoodles

all-purpose flour 2 teaspoons cream of tartar 1 teaspoon baking soda 1/2 teaspoon salt 1/2 teaspoon pumpkin pie spice 1 3/4 cups sugar, divided 2 sticks unsalted butter, softened 1 large egg 3/4 cup pumpkin puree 2 tablespoons ground cinnamon