Place the chopped potatoes in a large pot and add enough water to cover them. Bring to a boil and then reduce to a simmer until they are fork tender, about 15 minutes. Carefully drain the water and return the pot with the potatoes to the stove.

Add the milk and set the heat to medium. Do not boil. Bring the milk to steaming and barely simmering at the edges of the pan, for about 10 minutes.

Add salt and pepper to taste. Add the butter and stir gently to melt. Remove from heat and serve warm.