1. Preheat the oven to 350°F. Cut the eggplants diagonally into 1/2-inch thick slices. Brush both sides with olive oil and cook for 30 minutes on a baking sheet, flipping after 15 minutes.
2. To make the marinara sauce: In a large saucepan, heat the 4 tbsp of olive oil. Add the vegetables and cook over medium heat, stirring occasionally, for about 10 minutes.
3. Squeeze the tomatoes to remove the juice, then add them to the saucepan with the juice. Season and let simmer for 30 minutes.
4. Cook the rice in a 2L pot of boiling water for 15 minutes. Drain and return to the pot. Melt 3 tbsp of butter with saffron in a small saucepan. Add the parsley and stir into the cooked rice.
5. To make the bechamel sauce: Melt the butter in a saucepan over low heat. In another saucepan, heat the milk until almost boiling. Add the milk to the butter and saffron, still over low heat, and stir for 10 minutes. Add salt, pepper, and nutmeg; continue cooking until thickened, then remove from heat.
6. Increase the oven temperature to 375°F. Grease a 9×13 inch baking dish. Spread a thin layer of marinara sauce. Alternately spread one-third of the rice, half of the eggplant, and half of the remaining marinara sauce. Cover with the remaining rice and top with bechamel sauce. Sprinkle with parmesan.
7. Put the dish in the oven, reduce the temperature to 350°F, and cook for 30 minutes. Serve immediately.