Sauté onion in a large skillet in oil over medium heat. Add tomato purée, 2/3 cup water, oregano, salt, and pepper; bring to a boil. Reduce heat and simmer for 15 minutes.
Layer half each of eggplant and tomato mixture in a lightly greased 12x8x2-inch baking dish. Top with half of the shredded cheese, remaining eggplant, and remaining tomato mixture. Cover and bake at 350° for 55 minutes. Remove cover and top with remaining cheese; bake 5 minutes longer, or until cheese is melted.
Eggplant casserole serves 6.