Preheat oven to 375 degrees.
In a large skillet, brown beef with onion and bell pepper over medium-high heat; drain. Add salt, pepper, 1 cup of broth, garlic, tomatoes, eggplant, oregano, basil, and marjoram.
Bring to a boil then reduce heat and simmer for about 10 minutes, making sure eggplant doesn't become too tender (it will cook more in the oven!).
Whisk cornstarch and remaining broth together, and stir into beef mixture. Pour mixture into a 9- x 13-inch baking pan and sprinkle with cheese; bake for 10 minutes or until cheese is golden and melted, and eggplant is fork-tender.