Boil or steam the potatoes until they are tender. As soon as they are done, peel and mash them, preferably in a ricer.
Mix in the butter with a fork.
Heat the half and half until bubbles begin to form around the edges, then add it to the potatoes, mixing well.
Mix in the Parmesan cheese and season with salt and white pepper.
Serve at once or transfer to a buttered casserole, dust with additional cheese, and reheat for 15 minutes in a 350 F (180 C) oven.