Melt butter in a saucepan over medium heat.
Cook, stirring constantly, until: Foamy, golden brown, smells nutty, brown bits form at bottom
Immediately remove from heat.
Pour into a heat-safe bowl.
Cool 15–20 minutes until no longer hot. (It should be warm, not hot)
Add sugars to cooled brown butter.
Whisk until smooth and glossy.
Add eggs and vanilla. Whisk until slightly thickened.
In separate bowl whisk: Flour, cream of tartar, baking soda, salt, cinnamon
Add to wet mixture. Mix just until combined.
Chill dough 30–45 minutes. (Brown butter is liquid — chilling prevents spreading)
Preheat oven to 350°F.
Mix cinnamon + sugar for coating.
Scoop dough into 2 tablespoon balls.
Roll in cinnamon sugar.
Place on lined baking sheet.
Bake 9–11 minutes.
Edges should look set. Centers slightly soft.
They will continue setting as they cool.
Let rest in pan 5 minutes. Transfer to cooling rack.