Melt the butter, over medium-low heat, add the flour and stir until you get a wet paste with no lumps. Continue to cook for 1-2 minutes, while stirring to prevent it from burning. Slowly start adding the milk, a few tablespoons at a time, until it gets all incorporated. Season with salt, pepper and  freshly grated nutmeg.  

Preheat oven to 350 F.

Cut eggplants in half lengthwise, and using a sharp knife, make crisscross cuts into the flesh, about an inch deep. Brush the cut sides with 2 Tbs of olive oil, and sprinkle with salt liberally.  Place the halves, cut side down, on a baking tray, and roast for 30-40 minutes, or until the eggplant is soft.

Remove the eggplant from the oven, and scoop out most of the flesh.  Chop the eggplant pulp roughly and set aside.  Arrange the eggplant cavities in a baking dish.

While the eggplant is roasting, slice the onion in half, and then into half moons. Heat the remaining 2 Tbs of olive oil and add the onion. Cook on low heat for 15 minutes, until the onions have caramelized. Remove from pan and set aside. **

To the same pan, add the ground meat, season liberally with salt and pepper, and cook for a few minutes until browned. Add the can of chopped tomatoes, the tomato paste, the pressed garlic, oregano, cinnamon, and salt and pepper to taste.  Add the chopped eggplant flesh and the caramelized onions, and mix everything well. Cook for 5 minute, taste and adjust the seasoning if needed.  Remove from the heat, and spoon the mixture over the eggplant cavities, distributing it evenly (if you have left over filling, add it to the baking dish).  

Top each eggplant half with the bechamel sauce, and sprinkle the grated cheese on top.  Bake for 10-15 minutes until you get a nice cheesy crust.  Serve with chopped fresh oregano.