Prep the plums: Wash the plumbs and pat them dry. Cut them in half and remove the pits. Place the plum halves in a bowl and sprinkle them with the icing sugar. Toss and set aside.
Cook the potatoes: Wash and scrub the potatoes and cook them whole with skin on, in boiling water until fork tender. Depending on the size of the potatoes, this could take 40 to 60 minutes. Drain and let them cool.
Prepare the breadcrumb mixture: Melt the butter in a skillet. Add the breadcrumbs and brown for a few minutes over low heat, until the breadcrumbs start to turn golden brown. in a non-stick frying pan melt butter then add the breadcrumbs and brown it on low heat. Stir in the granulated sugar and let it cool completely. Set aside.
Make the dough: Once the potatoes have cooled enough to work with them, remove the skin, it should easily come off. Using a box grater, finely shred the potatoes into a bowl. To the same bowl (make sure potatoes have completely cooled), add the eggs, salt, flour, semolina and mix using a wooden spoon. The dough will be very sticky but homogeneous. In case your dough is too wet you could add a a tbsp of flour and a tbsp of wheat semolina but no more.
Boil water: Add water to a medium size pot and bring to a boil over high heat; when water start to boil add a tablespoon of vegetable oil to it.
Form the dumplings: With your hands slightly wet, divide the dough into 12 equal pieces. Using your hands, flatten each piece so that it's about ¼ of an inch in thickness. In the center of each piece, place half a plum, then seal it and shape it into a ball. Repeat with remaining ingredients.
Cook the dumplings: Place the dumplings into the pot with boiling water, 3-4 at a time, and cook them until they rise to the surface. Using a slotted spoon, take them out and place them directly into the skillet with the breadcrumbs mixture. Roll them around to make sure they are perfectly coated all around. Repeat with remaining dumplings.
Serve: Serve when completely cooled!