Cook lasagna in a large quantity of boiling water until just barely tender; drain off most of water; add ice cubes to stop cooking. (Allow lasagna to stand in cold water to prevent pasta sticking together.) In a saucepan, brown meat with onion and garlic; drain off fat. Cook over low heat, covered, for about 5 min. Stir in mushrooms with liquid, tomato sauce, tomato paste, salt and oregano. Simmer 15 mins. Combine egg with spinach, cottage and parmesan cheeses. Spread 1/3 of meat sauce in 13x9 in. baking dish. Cover 1/4 of lasagna (about 5 overlapping strips.) Alternate another 1/3 of sauce and 1/4 of lasagna. Spread spinach mixture over pasta and cover with 1/4 lasagna strips. Top with remaining sauce and pasta. Arange mozzarella cheese on top. Bake at 350F for 30 mins. Let stand 10 mins. before serving.