A touch of cream mellows and sweetens the fennel. Use a slotted spoon to drain the slices for serving, or spoon up the fennel with all its liquid and offer hot Tuscan bread to sop up the juices.
Preheat oven to 350F. Lightly rub 21/2-quart casserole with olive oil.
Slice away and reserve fronds from fennel bulbs. Cut thin slice off bottom of each bulb, and remove any bruised outer leaves. Mince enough of fronds to make 4 tablespoons, and discard remainder. Mix minced fronds with Parmigiano-Reggiano, and reserve.
Bring large pot of lightly salted water to a boil. Slice bulbs from top to bottom lengthwise in 1/2-inch-wide slices. Transfer slices to boiling water, and cook until half done, for about 5 minutes. Drain, and place slices in casserole. Add vegetable broth, cream, fennel seed, salt and pepper to casserole. Broth should partially cover fennel. Add more broth, if needed.
Bake for 20 minutes. Sprinkle with Parmigiano-Reggiano mixture, and bake for 15 minutes more, or until golden.
Remove from oven, and serve hot or lukewarm.