In your mixer, cream together the butter and 1½ cups of sugar. Reserve ¼ cup of sugar for the topping.
Add the eggs and vanilla, continuing to mix.
Add the flour, cream of tartar, baking soda, and salt. Mix until just combined. It will make a thick dough very quickly.
Wrap the dough in plastic wrap and chill in the fridge for 20 minutes.
Mix together remaining sugar and cinnamon to make a cinnamon-sugar topping. Pour this in a bowl or shallow dish, so you can roll dough balls in it.
Preheat oven to 350°F. Line your baking sheet with parchment paper.
Using a cookie scoop, scoop roughly 1 Tbsp balls of dough and form them into spheres. Roll these in the cinnamon-sugar topping and place on the baking sheet, roughly three inches apart.
Lightly press your thumb (or the back of a spoon) into the top of each ball to help flatten it slightly.
Bake for 9-10 minutes. The cookies will still be quite light and very soft, but trust me; they're done.
Let the cookies cool for at least 5 minutes before moving or eating, to allow them to solidify.