In a large bowl with a hand mixer or stand mixer fitted with a paddle attachment, cream the butter and sugar on high for 1 minute until the mixture is pale and fluffy.
Scrape down the sides and add in the egg and vanilla extract and mix just until combined.
In a separate large bowl, whisk together the flour, cream of tartar, baking soda, and salt. Add the dry ingredients to the wet ingredients in three different parts, mixing between each addition. Scrape down the sides a needed and mix until fully incorporated.
Chill the dough for 30 minutes before shaping. Meanwhile, mix together the sugar and cinnamon for the coating and set aside.
Preheat the oven to 375 degrees F and line a large baking sheet with parchment paper and set aside.
Use a tablespoon-sized cookie scoop to measure the dough, roll into balls and then roll each ball in the cinnamon sugar mixture before placing on the cookie sheet. Place cookies 2-inches apart and bake for 8 to 10 minutes.
Let the cookies cool on the baking sheet before transferring to a cooling rack. Cookies will be very warm and soft.