In a mid-sized mixing bowl, whisk together the flour, cream of tartar, soda and salt. Set aside.
In a mixing bowl or stand mixer, cream together the butter, sugar and eggs until the mixture is smooth and lightened in color. Add the flour mixture to the butter mixture and mix together until evenly and thoroughly combined. Chill the dough for 30 minutes.
Preheat the oven to 350°F.
Rub a cast-iron (or other oven-proof) skillet with a small amount of butter. Sprinkle 1 teaspoon of the cinnamon sugar mixture over the bottom of the skillet. Scrape the cookie dough into the pan. Moisten your hands with water and pat out the dough evenly, covering the bottom of the skillet completely. Evenly sprinkle the remaining cinnamon sugar over the cookie dough. Bake the cookie for 30-45 minutes. When the edges have browned and the center is golden brown the cookie is ready to be pulled from the oven. At this stage, the cookie, when sliced, will be very moist. If you like your cookies crispier, leave in the oven for closer to the 45 minute mark. When done to your liking transfer the pan to a wire rack to cool for 20 minutes. After 20 minutes, you can slice the cookie into wedges. This is best served slightly warm with ice cream melting over it. But really? What in life isn't better that way?