Chop onion and cabbage in to bite size pieces, set aside. In a medium sauce pan bring a quart of water to a boil. Cook cabbage in water. Remove cabbage from water and allow to cool.
In a skillet, brown ground beef, onions, salt, pepper and garlic. Strain the ground beef to remove the grease and add the mushrooms.While the beef is cooking, cook rice according to package instructions in a medium sauce pan. After the rice is fully cooked add the rice to the drained ground beef mixture.
Spread a small amount of sauce on the bottom of a casserole dish. Add a small layer of cooked cabbage followed by the meat mixture, ricotta or cottage cheese, mozz/prov cheese and top with another layer of cabbage. Then add another layer of sauce and repeat the layering of items. Top the last layer of cabbage with the remaining sauce or till lightly covered. Cover lasagna with foil and bake in 350 degree oven for 1 hour. After 1 hour remove foil, sprinkle with mozz/prov cheese and place back in oven for an additional 15 minutes or until cheese is lightly browned on top. Let stand for 5 minutes and serve.