Drain the boiled potatoes and let them cool slightly.
Mash the potatoes until smooth or pass them through a potato ricer for a finer texture.
In a large bowl, combine the mashed potatoes, all-purpose flour, salt, and egg.
Mix until a soft dough forms. If the dough is too sticky, add a little more flour, but be careful not to add too much as the dough should remain soft.
Divide the dough into smaller portions. On a floured surface, roll each portion into long, thin ropes about 1/2 inch in diameter.
Cut the ropes into 1-inch pieces to form the dumplings.
Bring a large pot of salted water to a boil.
Add the dumplings in batches, being careful not to overcrowd the pot. Stir gently to prevent sticking.
Cook the dumplings until they float to the surface, about 2-3 minutes. Remove with a slotted spoon and transfer to a plate.
In a bowl, combine the ground poppy seeds and powdered sugar.
Arrange the cooked dumplings on a serving plate.
Drizzle generously with melted butter.
Sprinkle the poppy seed and sugar mixture over the dumplings.
Enjoy your meal!