Melt the butter in a saucepan over medium heat. Stir constantly until it turns golden brown and smells nutty. Pour into a bowl and let it cool for 15 minutes.
Preheat the oven to 350 degrees Fahrenheit.
Mix the cooled brown butter with 1 cup granulated sugar and the brown sugar. Beat in the egg and vanilla.
Stir in the flour, cream of tartar, and baking soda until a dough forms.
In a small bowl, mix the remaining 2 tablespoons of sugar with the cinnamon.
Roll the dough into balls, then roll each ball in the cinnamon sugar mixture.
Place on a baking sheet and bake for 9 to 10 minutes.