Cut the eggplant in half lengthwise and remove the pulp, leaving a thin shell. Chop the pulp and place it in a bowl. Sprinkle with salt and let stand for 30 minutes. Sprinkle the shells with salt and let stand.
Sauté the ground beef, onion, green pepper and garlic in the 2 tablespoons of butter, stirring several times.
Rinse the eggplant pulp with cold water, drain, and add it to the meat mixture. Brown well.
Add the tomatoes with their liquid, the salt, pepper, parsley and rice. Cover and cook for 15 minutes, until the rice is almost cooked.
Rinse the eggplant shells and arrange them in a baking dish. Fill with the meat mixture.
Toss the bread crumbs in the melted butter and cover the filling with them. Sprinkle with the grated cheese.
Pour 1 cup of water into the baking dish. Bake, covered, at 350°F for 30 minutes.
Uncover and continue baking for 30 minutes, or until lightly browned.