In a small skillet over medium-low heat, melt the butter, stirring the pan frequently for even browning, until it smells nutty and most of the milk solids turn a shade of medium-brown. Immediately remove from the heat so the milk solids do not burn and transfer to a small heatproof bowl.
Make the roux: in a small pot over medium heat, whisk together the milk and flour until it thickens into a paste. Set aside.
Dissolve the yeast: combine the yeast, a sprinkle of sugar and warm water in the bottom of a stand mixer bowl and set aside for 5 minutes, until foamy.
Over the yeast add the remaining dough ingredients (except the butter) and the roux. Knead on low until it starts to form around the dough hook, then add the butter and knead on medium speed for 10-15 minutes, until the dough comes back together around the hook. It will still be sticky and mostly shapeless but formed into a ball. Set in an oiled boil and cover with plastic wrap to rise for about 1.5 hours, until it's about 50% puffier. At this point I prefer to set it in the fridge for an overnight chill, this helps with getting a better shape later.