Peel the onions. Peel the carrots. Finely dice both. Cover and simmer in 2 teaspoons of melted butter over medium heat for about 10 minutes. Season with salt, pepper and a pinch of sugar. Pluck the parsley from the stalks and chop. Mix half of the parsley into the onions and carrots.
Shape the dumpling dough into 8 equal sized dumplings. Press each of these flat between your hands, fill with 1 tablespoon of carrot mixture and close carefully.
Bring plenty of salted water to the boil in a large saucepan. Add the dumplings and let simmer for 20 minutes over a medium heat.
In the meantime, melt the rest of the butter and stir in the rest of the parsley. Take the dumplings out of the pot with a slotted spoon, drain and serve with the parsley butter.