Peel potatoes and cut into quarters. Boil until tender. Cool, then mash until smooth. Add eggs and salt; mix well. Work enough flour into potato mixture to make a smooth, firm dough. In a separate bowl mix sugar and cinnamon. Pit plums and fill each cavity with 1 teaspoon of the cinnamon-and-sugar mixture.
Take a piece of dough and pat it into a round cake 2-½ inches wide and about ¼ inch thick. Put one sugared plum in it, fold the dough over the plum, and pinch edges to seal, making a round dumpling. Repeat with the remaining plums and dough.
Drop dumplings one at a time into a large pot of boiling salted water, until water returns to the boil with all dumplings in the pot. Boil gently for 5 minutes, then turn down heat and simmer for about 15 minutes longer. Scoop out with a slotted spoon and place in serving bowl. Drizzle with melted butter, sprinkle with bread crumbs, and serve hot.