In a large pot, combine cabbage, onion, broth, butter, salt, and pepper. Simmer over medium heat until cabbage is tender, about 20 minutes.

In a bowl, mix flour, eggs, and milk until a soft dough forms.

Drop spoonfuls of dumpling dough onto simmering cabbage.

Cover and cook for 15 minutes without lifting the lid, until dumplings are cooked through.

Serve hot with extra butter if desired.