Place the potatoes in a large pot and cover with water by an inch. Bring to a boil over high heat, then reduce to simmer. Cook until the potatoes are fork tender, 25 to 30 minutes. Drain.
Return the potatoes to the pot and add the butter, milk and some salt and pepper. Mash the potatoes to the desired consistency. While still hot, fold the cheese into the mash and stir to melt.