Place the half peeled potatoes and 1 tablespoon of salt in a 4-quart saucepan with cold water to cover. Bring to a boil, lower the heat, and simmer covered for 25 to 35 minutes, until the potatoes are completely tender. Drain.
In a small saucepan, heat the half-and-half and butter. Transfer the potatoes to an electric mixer fitted with the paddle attachment and mix them for a few seconds on low speed to break them up.
Slowly add the hot cream and butter to the potatoes, mixing on the lowest speed. the remaining salt, and pepper; season, to taste, and serve immediately. If the potatoes are too thick, add more cream and butter.