In a bowl, beat egg whites and oil to blend. In another bowl, mix crumbs and fennel seed.
Rinse eggplant; trim and discard ends. Cut eggplant crosswise into 1/3-inch-thick slices. Trim stalks from fennel head; rinse and reserve 1/4 cup feathery green leaves. Trim and discard fennel root end, bruised areas, and coarse fibers. Rinse fennel and cut crosswise into 1/4-inch slices.
Dip eggplant in egg mixture, lift out, drain briefly, and coat with crumb mixture. Arrange slices in a single layer on a 12- by 15-inch baking sheet. Mix fennel, 1/2 at a time, with egg mixture. Lift out with a slotted spoon, drain briefly, then add to crumb mixture. Mix and lift from crumbs. Spread pieces in a single layer on another 12- by 15-inch baking sheet.
Bake in a 450° oven until vegetables are well browned and eggplant is soft when pressed, 15 to 20 minutes; if using 1 oven, switch pan positions after 7 to 9 minutes. Remove fennel from oven and discard any scorched crumbs. Sprinkle eggplant with 1/2 the cheese. Bake until cheese is lightly browned, 3 to 4 minutes more.
Meanwhile, in a 1- to 2-quart pan over medium-high heat, stir pasta sauce and wine until boiling, 2 to 4 minutes.
Arrange equal amounts of eggplant and fennel on warm dinner plates; garnish with fennel leaves. Sprinkle with remaining cheese. Spoon sauce onto plates; add salt and pepper to taste.