Preheat the oven to 450°F. Bake the potatoes until tender, about 1 hour. Let stand until cool enough to handle, then cut the potatoes in half and scoop out the pulp. Put the pulp through a potato ricer or through the large holes of a food mill, or mash (do not puree in any piece of electric equipment). Measure about 3 cups.
Combine all ingredients except the bread crumbs and oil. Shape into 1½-inch balls and roll in the bread crumbs to coat.
Preheat the oven to 300°F. Heat 4 to 6 inches oil in a deep fryer or heavy deep saucepan over medium-high heat to 350°F. Add as many croquettes as will comfortably fit without crowding and fry, turning occasionally, until golden brown, about 5 minutes. Drain on paper towels and keep warm in the oven (no more than 15 minutes) while frying the remaining croquettes. Serve with steak, lamb, or whatever your heart desires.