Heat the oven to 425°F. Brush eggplant with oil, season with 1 teaspoon salt and roast on sheet pans for 20 minutes. Reduce oven to 375°F.
Brown beef and onion and drain. Add garlic and tomato paste for 1 minute, then tomatoes, cinnamon, remaining salt and pepper and simmer 8 minutes.
Melt butter, stir in flour for 1 minute, whisk in milk and simmer until thick. Cool 5 minutes, then whisk in eggs and 1/2 cup Parmesan.
Layer half the eggplant, all the beef sauce and remaining eggplant in a greased 9-by-13-inch dish. Spread béchamel on top and sprinkle with remaining Parmesan.
Bake 45 to 50 minutes until golden. Rest 20 minutes before cutting.