Cut peppers in half lengthwise; remove and discard seeds and membranes. Place peppers, skin side up, on a baking sheet, and flatten with palm of hand. Broil 5 1/2 inches from heat (with electric oven door partially opened) 15 to 20 minutes or until charred. Place in ice water until cool; peel and discard skins. Coarsely chop peppers.
Combine tomatoes and 1 cup boiling water in a small bowl; let stand 5 minutes. Drain.
Position knife blade in food processor bowl; add chopped pepper, tomatoes, basil, and next 4 ingredients. Process until smooth, scraping sides of processor bowl once. Combine pepper mixture, tomato sauce, and 2 tablespoons water; stir well. Set aside.
Beat cream cheese at medium speed of an electric mixer until creamy. Add ricotta cheese, sour cream, egg substitute, Parmesan cheese, and oregano, beating until smooth. Set aside.
Coat a large nonstick skillet with cooking spray; place over medium-high heat until hot. Add mushrooms, carrot, zucchini, and onion; saute 8 minutes or until tender.
Spread 3/4 cup pepper mixture over bottom of a 13- x 9- x 2-inch baking dish coated with cooking spray. Place 3 lasagna noodles over sauce; top with half of cream cheese mixture, half of vegetable mixture, and half of remaining pepper mixture. Repeat layers with remaining noodles, cream cheese mixture, vegetable mixture, and pepper mixture.
Cover and bake at 350° for 30 minutes. Uncover; sprinkle with mozzarella cheese. Bake 5 additional minutes or until cheese melts. Let stand 10 minutes before serving.