Before you start cooking: First, boil 3 medium potatoes in their skins ahead of time. Allow them to cool completely before using. Clean 12 pieces fresh plums, pat them dry, then halve and pit them.
Peel the cooled potatoes and finely grate them. In a bowl, combine the grated potatoes with 1 ½ cups all-purpose flour, 1 egg, 7 ounces cream cheese, and ¼ teaspoon salt.
Knead the mixture into a smooth, non-sticky dough. If needed, add a little more flour to achieve the right consistency.
Shape the dough into a cylinder and cut it into equal-sized pieces on a floured surface.
Lightly press each piece of dough into the flour on both cut sides and shape it into a flat patty.
Wrap a halved plum in each piece of dough, shaping it into a round dumpling.
Cook the plum dumplings in gently boiling, salted water for 8-10 minutes. There is no need to flip them during cooking.
Serve the plum dumplings sprinkled with ground poppy seeds and powdered sugar. As a final step, drizzle melted butter over the top.