Form the dough into a thick log on a lightly floured surface and cut into 12 equal pieces. Flour your hands, and roll each piece between your palms into a ball. Set aside on a lightly floured kitchen towel on a baking sheet.
Bring a large pot of lightly salted water to a boil over high heat. One at a time, place the dumplings in the water. Cover the pot to return the water to the boil. Reduce the heat to medium. Simmer, uncovered, until the dumplings are cooked through, about 10 minutes. Using a slotted spoon or wire skimmer, transfer the dumplings to a clean kitchen towel to drain.
Place 2 or 3 dumplings in each bowl, drizzle with the butter, and sprinkle with the nuts. Sift confectioners’ sugar over the top and serve hot, with the plums passed on the side.