Preheat your oven to 400°F. Cover two cookie sheets with parchment paper or a silicone baking mat.
In a stand mixer, using the paddle attachment, cream butter, shortening, and sugar. Beat in egg and vanilla.
Scrape down the sides and bottom of the bowl. On low, mix in flour, cream of tartar, baking soda, and salt until just combined.
In a small bowl, mix 2 tablespoons of sugar with the cinnamon. Scoop 36 1/2-ounce mounds of dough into balls (just over 1-inch wide) and roll in sugar mixture. Place on a baking sheet 1 1/2-inches apart. These are small cookies, so you should be able to fit 18-20 on a standard-size cookie tray.
Bake for 6 to 8 minutes. They are done when they are just golden and look set. You don't want them to crisp up too much since we are turning them into sandwiches.
Allow cookies to cool completely.