In your small saucepan, brown the butter until it's just past amber. Turn off the heat and swirl it until it's a darker brown but not quite burnt. Pour into a small bowl, and move to the fridge for 45 to 50 minutes or until just set. It should be 72ºF or room temperature.
Preheat the oven to 350ºF.
In a small bowl, pour out your sprinkles and set aside.
In the bowl of your stand mixer, cream together the browned butter and brown sugar until light and fluffy, roughly 5 minutes.
Add in the milk, flour, salt, and cream of tartar. Mix until well combined.
Scoop out 12 large cookie dough balls. Roll each between your hands to smooth them out and then toss in sprinkles to coat.
Set the balls on your cookie sheet 2 inches apart. Bake 12-14 minutes.