Preheat oven to 350°F. Butter an 8 x 8-inch or a 9 x9-inch casserole with 1 tablespoon of the butter.
Peel and quarter the potatoes and add them to a large stock pot.
Bring the pot to a boil and boil the potatoes for about 15 minutes.
Melt the butter. Using a hand mixer or a potato masher, add to the potatoes and mash coarsely.
Fold the chopped chives, dry-cured ham or prosciutto if using, and the green parts of the scallions into the mashed potatoes.