Place the potatoes, skins on, in a large pot and cover with cold water. Bring to a boil and add 2 1/2 tablespoons salt. Reduce heat and simmer until just tender, about 15 minutes. Drain the potatoes and return to the pot. Add the butter, buttermilk, cream, nutmeg, 1/2 teaspoon salt, and 3/4 teaspoon pepper. Mash the potatoes with a handheld masher. Fold in the chives before transferring to a serving dish.
Make-Ahead Note: The potatoes can be made up to 2 hours in advance and kept warm in a double boiler or Crock-Pot. If the potatoes are chilled and then reheated, they will turn dry and pasty.