Whisk together the flour, salt, cream of tartar, and baking soda in a bowl and set aside.
Brown 1/2 cup butter in a saucepan, swirling, until butter foams and starts to turn brown and smells nutty. Immediately transfer butter to a liquid measuring cup and see how much water content you lost. You want to have 1/2 cup of butter, so stir in the remaining 1-2 tablespoons of butter if you need it – the butter should just melt, not foam.
When the butter is mostly cool, whisk in both 1/3 cup of brown and white sugar until incorporated with no lumps. Whisk in the egg until smooth and glossy. Stir in the vanilla and use a rubber spatula to fold in the dry ingredients until just combined and no dry spots remain. Do not over mix.
Mix the cinnamon and sugar in a small bowl. Use a 1.5 tablespoon cookie scoop and scoop out two balls of dough, so that each cookie is 3 tablespoons large. Smoosh the two balls on top of each other – they should kind of look like a 2 ball snowman (see photo) and you should get about 8-10 cookies. Roll the logs/tots generously in the cinnamon sugar, being sure to coat evenly. Place the cookies on a parchment paper lined cookie sheet, cover with plastic wrap and let chill in the fridge for 15-30 minutes
Heat the oven to 325°F and bake on a parchment paper lined baking sheet for 12-15 minutes or until the edges are just set, rotating and moving trays halfway if browning unevenly. Remove from the oven and bang the pan down against the counter top (this helps create a couple of ripples like you see on Instagram) Let cool on the baking sheets for 5 minutes, the move to a rack to cool completely. Enjoy!