Heat oil in large skillet. Cook onions, garlic and mushrooms until soft, about six minutes. Stir in tomatoes and oregano and simmer 10 minutes. Taste for salt and pepper and set aside.

Soften matzohs by holding under warm running water for a few seconds. Spread two tablespoons tomato sauce on bottom of pan. Layer matzohs alternately with mushroom-onion mixture and jack cheese ending with a layer of matzoh on top. Pour remaining tomato sauce over all, sprinkle with Parmesan cheese and bake about 30 minutes or until bubbly. Let cool slightly and cut into squares to serve.