Place the butter and cane sugar in a bowl with a hand mixer and cream together. Add in the egg and beat in, creating a fluffy, smooth base.
In a separate bowl, whisk together the flour, cream of tartar, baking soda and salt. Slowly add in the flour mixture to the butter mixture, mixing until just combined and a dough has formed.
Place the dough in the fridge to chill for 15 minutes.
Preheat the oven to 350 degrees F. Remove the dough from the fridge and lightly grease a baking sheet or line with parchment paper.
Combine the remaining sugar and cinnamon together in a bowl. Using a 1 tablespoon scoop, scoop out dough and roll into a ball. Roll into the sugar/cinnamon mixture and place on the baking sheet.
Continue with the rest of the dough, leaving 2" between the balls as they will spread as they cook. Depending on the size of your baking sheet, you may need more than one.
Bake for 10 minutes, then remove from the oven and promptly place a chocolate kiss in the center of the cookie. Let cool completely and enjoy!