If flat, no-boil lasagna noodles are not available, use traditional ruffle-edged lasagna noodles, precooking them according to package directions. Cut to fit an 8-inch square baking dish.
1. Preheat oven to 450°F. Coat two roasting pans and one 8-inch square baking dish with cooking spray.
2. Place eggplant in one roasting pan and sprinkle with 1/2 tsp. salt and 1/4 tsp. freshly ground pepper. Place tomato halves in second roasting pan, skin side up. Roast eggplant and tomatoes until tender, tossing eggplant occasionally, 30 to 40 minutes. Remove and discard tomato skins. Reserve 1/4 cup tomatoes. Place eggplant, remaining tomatoes and their juices in a large bowl. Add basil and toss, using spatula to break up tomatoes; set aside. Reduce oven temperature to 375°F.
3. Steam spinach or chard until wilted, 4 to 6 minutes; set aside to cool. Chop.
4. In a large bowl, combine mozzarella, ricotta, tofu, 1 Tbs. Parmesan and egg white; mix well.
5. Place 2 lasagna noodles in bottom of prepared baking dish. Top with half of the cheese mixture, half of the eggplant strips and half of the spinach. Repeat layers, and top final layer of pasta with reserved 1/4 cup tomatoes. Sprinkle with Asiago cheese and remaining 1 Tbs. Parmesan. Loosely cover lasagna with aluminum foil and bake 30 minutes; uncover and continue baking until cheese is golden, about 15 minutes more. Let stand 15 minutes before serving.