Place the potatoes (whole) in a large pot and add enough cold water to cover. Bring to a boil and add 2 teaspoons salt. Reduce heat and simmer until very tender, 35 to 40 minutes. Drain the potatoes; reserve the pot. Once they are cool enough to handle, peel the potatoes and return them to the reserved pot with the butter, 11/2 teaspoons salt, and 1/4 teaspoon pepper. Mash until fluffy and well combined.
Add the half-and-half and mash just enough to combine.