Using mixer, cream butter for about 1 minute on medium speed until smooth.
Add the sugars on medium speed until fluffy and light in color. Mix in the egg and vanilla. Scrape down the sides as needed.
In a medium bowl, mix together the flour, cream of tartar, baking soda and salt.
With the mixer on low speed, slowly add the dry ingredients to the wet ingredients and mix together until dough comes together.
Roll approx 2 tablespoons of dough into a ball (or use a medium ice cream scooper, I used 1.5 tablespoons) and roll in the cinnamon-sugar mixture. Dough is sticky, so using a scooper makes it much easier than rolling. If you don't have a scooper, put the dough in the fridge for 15 - 30 minutes and rolling will be easier. (For even thicker cookies, chill in the fridge for 1-2 hours or until firm. This step results in thicker cookies that will spread less while baking.or longer.)
Place cinnamon-sugar balls on a plate or cookie sheet and place in fridge while you preheat your oven.
Preheat oven to 375 degrees.
Line two cookie sheets with parchment paper and then place cinnamon-sugared cookie balls on baking sheets.
Bake for about 8-10 minutes, until cookies begin to brown at the edges but the center is still soft. Cookies will appear undone but will continue to bake on the warm baking sheet. (It's better to under-bake the cookies, rather than over-bake.) Leave cookies to cool on baking sheet for 10 minutes, then gently transfer to a wire rack to cool completely.
Store cookies at room temperature in an airtight container for up to 3 days. Cookies can also be frozen for up to 2 months.
Cookies pictured were chilled while the oven was preheating.