2. Slice unpeeled eggplants and cut into 1-inch cubes. Place in a colander, sprinkle with salt, cover with a weighted plate, and let stand for 30 minutes.
3. Heat oil in a heavy skillet. Carefully dry eggplant pieces and add to the skillet. Cook over high heat, stirring occasionally, until lightly browned.
4. Add onion, garlic, green pepper, oregano, and bay leaf while stirring. Stir in tomatoes and reduce heat. Simmer for 5 minutes, or until most of the liquid has evaporated.
5. Pour vegetable mixture into a casserole and stir in the rice and boiling chicken stock. Season with salt and pepper. Sprinkle with cheese and dot with butter.
6. Bake, uncovered for 30 minutes, or until the liquid has been absorbed by the rice.