Bring a pot of lightly salted water to a boil and cook the potatoes, covered, for about 30 minutes, or until soft when pierced with a skewer. When cool enough to handle, peel and mash them in a bowl.
Add the egg, egg yolk, and 1 tablespoon salt. Mix well. Start adding the flour, gradually, until you get a soft dough. The amount of flour needed depends on the potatoes you use. I needed 3 1/2 cups.
Transfer the dough to a floured surface and knead until smooth and firm. It shouldn't be sticky. Divide into two parts.
Working with one dough piece at a time, roll it out to 1/3 thick and cut into even squares. The size of the squares depends on the size of your plums. Mine were 3 1/2 inch (9cm).
Place a plum into the center of each square. Fold the dough in around the plum and seal the edges. Form a ball. Repeat with all the remaining dough.
Drop the dough balls into boiling water and cook for 10-15 minutes. They will rise to the top when done. Remove with a slotted spoon.
Melt the butter in a large skillet and stir in the breadcrumbs. Mix well. Roll the dumplings in the mixture to coat. Sprinkle with some cinnamon sugar if desired and serve. Enjoy!