Wash and dry the Zampone. Prick the Zampone about 20 times all over with a needle. Place in a pot large enough to submerge the sausage in water. Fill the pot with warm water and bring to just a boil. Lower the heat slightly, so the water remains almost boiling. Cover and continue cooking for 1-1/2 hours.
Uncover and check the internal temperature of the sausage with a meat thermometer. Cook until the temperature reads 150 degrees. Turn off the heat and let stand.
In a 12- to 14-inch non-stock saute pan, melt the butter over medium heat. Add the potatoes and saute slowly until lightly browned on all sides. Add the milk and simmer uncovered, until softened, about 10 minutes. Season with salt and pepper. Allow to stand in a warm place.
In a medium mixing bowl, stir together the mustard and vinegar. Slowly add the extra virgin olive oil in a thin stream, forming an emulsion. Stir constantly until all the oil is added. Add the snipped chives and check seasoning.
Remove the Zampone from the water. Carefully slice half the sausage into 1/2-inch rounds. On a large serving platter, spread the potatoes around the base. Place the Zampone pieces and slices over the potatoes. Pour the vinaigrette into a serving pitcher, allowing each person to dress his or her own portion. Serve immediately.