Preheat oven to 350. Mix flour, cream of tartar, baking soda and salt in a medium bowl.
Cream butter and sugar together in a mixer until they are light and fully combined – you will probably have to scrape down the sides of the bowl a few times.
Add the egg and vanilla and mix until combined.
Add the flour and mix until it is combined. The dough is going to look like large crumbs – don’t worry!
Scoop out level tablespoonfuls of the dough and squeeze and roll it together into balls.
Combine the remaining 1/4 cup of sugar with the cinnamon and roll the dough balls in the cinnamon sugar until they are coated completely.
Place the cookie dough balls 2 inches apart on parchment-lined cookies sheets. Flatten them gently with the bottom of a glass, and sprinkle with any extra cinnamon sugar.
Bake for 10 to 12 minutes. Tops should be crackly and a little puffy. Cool for 2-3 minutes on cookie sheets and then cool on racks. Make sure you eat one (or two!) while they are still warm!