1. Trim off feathery fennel greens and finely chop enough to make 1/4 cup; reserve for garnish. Save remaining greens for other uses. Trim off and discard tough stems, root ends, and any bruised spots from fennel heads. Cut fennel lengthwise into 1/2-inch-thick slices.
2. In a 6- to 8-quart pan over medium-high heat, combine oil and onion. Stir often until onion is limp, 5 to 7 minutes.
3. Add sliced fennel and wine. Cover and simmer over medium heat, stirring occasionally, until fennel is just tender when pierced, about 25 minutes.
4. Arrange fennel slices neatly in a shallow 3- to 3 1/2-quart casserole and add liquid. Cover tightly with foil.
5. Bake in a 375° oven until fennel is very tender when pierced, 1 hour and 10 minutes (1 hour in a convection oven).
6. Uncover fennel, sprinkle with cheese, and, if desired, broil about 4 inches from heat until slightly browned, 3 to 4 minutes. Sprinkle with reserved 1/4 cup chopped green fennel tops. Season to taste with salt.