On a well-floured work surface, roll out the dough to ¼inch thick. Using a 3-inch round biscuit cutter, cut out rounds. Gather up the scraps and reroll until all the dough has been cut out. You should have about 30 rounds.
Place about ½teaspoon prune butter in the center of each round. Brush water on the edges, then fold over into half-moons, pinch the edges closed, and press the seal with the tines of a fork. Place on a lightly floured kitchen towel on a baking sheet.
Bring a large pot of lightly salted water to a boil over high heat. A few at a time, add the dumplings to the water. Cover to return the water to a boil. Reduce the heat to medium and cook until the dumplings are cooked through, about 4 minutes. Drain well.
Meanwhile, melt the butter in a medium skillet over medium heat. Add the bread crumbs. Cook, stirring often, until the crumbs are golden and crisp, 3 to 5 minutes.
To serve, place 3 or 4 dumplings each in soup bowl, sprinkle with the bread crumbs, sift with the confectioners’ sugar, and serve immediately.