Whisk an egg with salt, nutmeg, milk and oil. Work in the flour with a wooden spoon until there are no more lumps.
Quickly prick small dumplings out of the dough with two small spoons and let them slide into the boiling water. When cooking, the dumplings get bigger. As soon as they swim up, they are done. Then drain and rinse with cold water if necessary.
Beat the remaining eggs, season with salt and whisk well.
Heat the butter in a pan and toss the dumplings in it. Pour the eggs over the dumplings and let them set. Serve with chives.
A green salad with a simple vinegar and oil marinade goes particularly well with it.