Peel the potatoes before cooking if you like. If you’re in a hurry, halve or quarter larger ones. Cut or whole, the idea is to have all the pieces about the same size. Put them in a large, deep pot and cover with cold water. Add a large pinch salt and bring to a boil.
Keep the water rolling until the potatoes are done, anywhere from 15 to 30 minutes, depending on the size of the pieces. The potatoes are done when a skewer or thin-bladed knife inserted into one meets almost no resistance. Drain the potatoes well and let them dry out a bit.
While the potatoes are draining, wipe the pot dry and put it back on the stove over medium-low heat. Add the milk and the butter and sprinkle generously with salt and pepper. When the butter is almost melted, remove the pot from the heat. Rice the potatoes into the milk mixture, run them through a food mill set over the pot, or add them to the milk mixture and mash with a fork or potato masher. Return the pot to the heat and stir constantly with a wooden spoon to reach the desired consistency, adding more milk if necessary. Taste, adjust the seasoning.