Preheat oven to 350F. Brush 2 quart casserole (oblong, preferably) with 1 tbs oil. Combine bread crumbs, oregano, salt, pepper and 1/4 cup Parmesan cheese. Cover dish bottom with one layer zucchini and squash. Brush with some of remaining oil. Sprinkle with 2 tablespoons bread crumbs. Add 2 more layers of zucchini and squash, oil and bread crumbs. Top with onion slices.
Make one more layer of vegetable. Cover with foil. Bake until tender, about 1 hour (check). Uncover, top with rest of crumbs and cheese. Broil until brown, about 5 minutes.
Cajun Country -- New Iberia, Louisiana