Scrub and peel the potatoes, then cut them into pieces all approximately of the same size and place them into a large pot.
Cover with cold water, then bring to a boil; slightly reduce heat and gently boil until tender, about 20 to 25 minutes.
While potatoes are cooking and almost done, in a saucepan combine the half and half, butter, salt, and pepper and simmer until melted and combined; set aside and keep warm.
When potatoes are tender, drain well.
Pass the potatoes through a food mill or mash with a potato masher (do not use an electric mixer).
Gradually add the warm liquid mixture to the milled/mashed potatoes, stirring, until you've added enough liquid to achieve the consistency you prefer (you might not need all the liquid).
Adjust salt and pepper to taste, if necessary, and serve.
Note: this is an excellent basic recipe you can add other tasty ingredients to, such as roasted garlic, crumbled blue cheese or gorgonzola, chopped or minced scallions/basil/parsley, caramelized onions or leeks.