In a medium mixing bowl, cream together the butter, shortening, and sugar for 2-3 minutes until light and fluffy using a hand mixer or stand mixer with a paddle attachment. Beat in the egg and vanilla extract, scraping down the sides of the bowl with a rubber spatula as needed.
In a separate bowl, sift the flour, cream of tartar, baking soda, and salt. With the mixer on low speed, slowly add the dry ingredients into the wet ingredients and mix until fully combined. Be sure to scrape down the sides of the bowl as needed. Chill the dough in the refrigerator for at least 30 minutes.
Preheat the oven to 400°F and prepare a greased cookie sheet. In a small bowl, combine the additional sugar and cinnamon for the coating. Roll the dough into 2-inch balls and coat thoroughly in the cinnamon-sugar mixture before placing them on the cookie sheet. Bake for 6-8 minutes.
Notes
Baking time may vary slightly depending on your oven. For a lighter, chewier cookie, bake for 6 minutes. For slightly crispier edges, bake for 8 minutes.
The dough can be prepared ahead of time and stored in the refrigerator or freezer until you are ready to bake the cookies. If frozen, allow the dough to thaw before baking or add an additional 1-2 minutes to the bake time.