Peel 2/3 of the potatoes, wash them well and drain. Grate the potatoes in a bowl filled with water and drain again using a clean cloth.
Peel the remaining potatoes, cut into dices and cook in salted water. Once they are soft enough, puree the potatoes and gently heat the puree.
In a bowl, stir together the puree and the grated potatoes. Season with salt and pepper
Mince the onion, garlic and herbs. Melt some butter in a skillet and brown the onion and herbs. Add them to the potato mixture.
Fold in the flour, eggs and one pinch of nutmeg. If the mixture is too sticky, add more flour. To make the dumplings, shape small balls (5 cm) of puree. Set aside
For the sauce: Heat 2 tbsp of olive oil in a saucepan. Add the pumpkin puree, sugar, white-wine vinegar, nutmeg, half-and-half, and the Pecorino. Season to taste. Stir sauce until heated through. Keep the sauce warm until the dumplings are ready.
In a large saucepan, boil enough salted water. Cook the dumplings in batches by dropping them in the water. Cook for about 10-15 minutes, or until they pop back up to the top
Place the dumpling on a plate or in a bowl, and cover with pumpkin sauce. Sprinkle with fresh parsley.