In a medium, cream the butter, brown sugar and white sugar with an electric mixer for about 4 minutes.
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 350 degrees.
In a small bowl, mix the sugar with the cinnamon for the topping.
Roll about 1 ½ tablespoons of the dough into a ball.
Then roll this ball in the cinnamon & sugar mixture and place on an ungreased cookie sheet. For a flatter cookie, press down the center a little.
Bake for 8 to 10 minutes until the edges are just light golden in color. They need to be soft so watch carefully the last couple of minutes.