In a saucepan combine potatoes and water to cover and bring to a boil.
Cook until potatoes are tender when pierced with a fork (about 40 minutes); drain.
When potatoes are cool enough to handle, peel and, while still warm, press through a potato ricer into a large mixing bowl.
Add salt, eggs, and the 1 tablespoon butter to potatoes and mix well.
Gradually mix in the 1 cup flour and farina until dough is easy to work, adding more flour if it is too wet. Turn dough out onto a floured board and knead well until smooth and fairly soft (5 to 10 minutes). With your hands form dough into a large sausage-shaped roll.
Cut roll into 12 to 16 equal pieces.
Cut open plums and remove pits.
Replace each pit with a sugar cube and re-form plum.
With a floured rolling pin, roll out each dough piece into a 3-inch square 1/4 to 1/3 inch thick.
Place 1 plum in center of each square. Bring up corners of square to enclose plum completely; no part of plum must be exposed.
Pinch dough edges together firmly so that dumpling doesn't break open during cooking.
Meanwhile, fill a large saucepan with water and bring to a boil over high heat. Drop in dumplings, being careful not to crowd pan, and boil gently, stirring occasionally.
Do not boil too hard or dumplings may split open.
Once dumplings rise to surface, cook until tender (5 to 10 minutes total cooking time, depending on intensity of boil). With a slotted utensil carefully remove dumplings one at a time to a heated bowl; cover tightly to keep warm.
Repeat with remaining dumplings.While dumplings are cooking melt the 1/2 cup butter in a small skillet over medium heat. Add bread crumbs and cook, stirring, until browned.
Turn out onto a flat plate. Roll hot dumplings in browned bread crumbs to coat completely and serve immediately.
Variations: Potato Noodles - Omit plums and sugar cubes.
Prepare dough as directed, but roll with your palms to form 2 or more sausage-shaped rolls about 1/2 inch in diameter.
Cut rolls into 2-inch lengths.
Fill a large saucepan with salted water and bring to a boil over high heat. Drop in noodles and cook until tender (5 to 10 minutes). Drain and roll in breads crumbs as directed for dumplings.
Dessert Potato Noodles Prepare Potato Noodles and roll in bread crumbs as directed.
Sprinkle with ground cinnamon and sugar to taste. Yield: 14 servings.