In a medium, cream the butter, brown sugar and white sugar with an electric mixer. Add the egg and vanilla and mix until smooth. In another bowl, mix the flour, baking soda, cream of tartar and salt. Pour the dry ingredients into wet ingredients and mix thoroughly. Refrigerate the dough for 30 minutes. Preheat oven to 300 degrees. In a small bowl, mix the sugar with the cinnamon for the topping. Roll about 1 1/2 tablespoons of the dough into a ball. Then roll this ball in the cinnamon & sugar mixture and place on an ungreased cookie sheet. Bake for 12 to 14 minutes.