WALNUT SAUCE WITH FENNEL: Put the walnuts, garlic and bread crumbs in a food processor and process briefly until everything is the texture of fine crumbs. With the motor running, gradually pour in about 1 cup of the water. Stop and scrape down the sides, then add enough water until it is the consistency you want. (It will thicken somewhat as it sits.) Stir in the oil and fennel seeds and season to taste with salt and pepper.
THE EGGPLANT: If the eggplant is mature with lots of developed seeds when sliced, lightly salt the slices and let them sit for 30 minutes. Blot with paper towels to draw off bitter juices. If the eggplant is light-colored and firm, without the presence of large seeds, just slice it and go onto the next step. Preheat the broiler. Brush both sides of the eggplant generously with oil. Place about 3 inches from the heat source and broil until golden brown. Turn the rounds over and broil until nicely colored and tender. If the eggplant looks dry, brush a little more oil over the top. Set the broiled eggplants on a platter and spoon a little of the walnut sauce over the tops. Season with pepper and garnish with the fennel leaves or parsley. Serve hot or slightly cooled.
(NOTE: If you are not planning to use the sauce right away, omit the garlic and add it just before you use it. This way the sauce will keep well for at least a week, refrigerated)