Boil the onions (preferably flatter white summer onions) until they can be easily pierced with a wooden toothpick. Cut in half horizontally and hollow out.
Finely chop the herbs (parsley, sage, rosemary, thyme, basil, mint, arugula, celery leaves or other herbs, as desired) together with the hollowed-out center of the boiled onions. Brown in butter and salt to taste. Soak the breadcrumbs in milk. Plump the raisins in warm water. Mix the herbs and chopped onion with the breadcrumbs and raisins, 2 eggs and about 2 tablespoons of grated cheese.
Stuff the boiled onions with this mixture and arrange in a baking pan or oven-proof dish. Meanwhile, beat 2 eggs with 1 ¾ cups of grated Parmigiano-Reggiano and a little milk. Pour the mixture over the onions to almost cover them. Place a pat of butter on each onion.
Bake in a moderate oven (350° F) until the top is golden brown.