1. Preheat oven to 450 degrees. Butter a four-quart ovenproof dish. On a baking sheet, toss the eggplant with 6 tablespoons oil and 1/2 teaspoon each salt and pepper. Spread in a single layer, and roast in the oven until soft and golden, 20 to 30 minutes. Transfer eggplant to the prepared dish, spreading in an even layer.
2. In a large saucepan, warm the remaining tablespoon oil over medium heat. Add the onions, garlic, and ground meat; cook, stirring to prevent sticking, until meat is browned, 5 to 7 minutes. Stir in the drained tomatoes, tomato paste, parsley, oregano, cinnamon, and 1/4 teaspoon each salt and pepper. Simmer, crushing tomatoes with the edge of a spoon, 15 minutes. Spread the mixture evenly over the eggplant.
3. Heat broiler. In a small bowl, mix the ricotta, feta, egg, 1/8 teaspoon pepper and a pinch of salt. Pour the mixture over the casserole, and spread evenly to the edges. Broil until topping is browned in spots, 5 to 10 minutes. Serve hot.