1. Preheat the oven to 365 degrees Fahrenheit. Cream butter and both sugars using a handheld or stand electric mixer.
2. Add vanilla, egg, cream of tartar, baking soda, and salt and mix well.
3. Gradually add flour until combined.
4. Roll dough into balls and place on ungreased cookie sheets approximately two inches apart.
5. Dip the bottom of a small round jar or glass into the granulated sugar (you may have to get it a little bit wet first) and flatten each cookie with it.
6. Bake for 10-12 minutes. Allow to cool partially on cookie sheets, then transfer to metal racks to cool completely.