Prepare Brown Butter: In a saucepan, melt the butter over medium heat. Allow it to cook, swirling the pan occasionally until the butter turns a golden brown color and releases a nutty aroma. Remove from heat and let it cool slightly.
Whisk Dry Ingredients: In a mixing bowl, whisk together flour, cream of tartar, baking soda, and salt. Set aside.
Combine Butter and Sugar: In a large mixing bowl, combine the browned butter and sugar. Mix until well combined.
Add Eggs and Vanilla: Beat in the eggs, one at a time, followed by the vanilla extract. Mix until smooth.
Incorporate Dry Ingredients: Gradually add the dry ingredient mixture to the wet ingredients, mixing until just combined. Do not overmix; the dough should be soft and slightly sticky.
Preheat Oven: Preheat the oven to 375°F (190°C). Line baking sheets with parchment paper.
Prepare Rolling Mixture: In a small bowl, combine the rolling sugar and ground cinnamon.
Form Dough Balls: Scoop out portions of the dough and roll them into 1-inch balls. Roll each ball in the cinnamon-sugar mixture until coated evenly.
Place on Baking Sheets: Place the coated dough balls on the prepared baking sheets, leaving space between each for spreading.
Bake: Bake in the preheated oven for 9-11 minutes or until the edges are set and the cookies appear slightly cracked on top.