Cook the peeled, cubed potatoes in boiling salted water until tender.
Use a handheld potato masher to mash the potatoes thoroughly.
While the potatoes are cooking, simmer the milk and scallions together for about five minutes. Do not let the milk boil, keep it at a low simmer only.
Add the hot milk and scallions, salt, pepper, and 4 tablespoons of the butter. Stir until the butter has melted and everything is well combined.
Melt the remaining two tablespoons of butter. Keep it warm to use for serving.
Serve the champ piled high on the plate with a well of melted butter in the center. Eat from the outside, dipping each spoonful into the well of melted butter.