We heat the pot, covered, over medium-high heat until the water comes to a boil. We remove the cover, stir, and continue to cook over medium heat until the potatoes are tender. This takes another 30 minutes or so, depending on the size of the potato pieces.
We drain the cooked potatoes into a colander and place back in the hot pot. We place the stick of butter in our serving bowl (which we can place above a pot of simmering water to keep the potatoes warm for a few minutes until it is time to eat). Using our ricer, we rice the potatoes right into the serving bowl. We add salt and pepper and some of the cold milk and mix with our hand mixer. We gradually add in the milk until the desired creaminess is reached.
We season to taste and then keep warm in the serving bowl, covered with foil, over a pot of simmering water.