Peel the eggplants using a vegetable peeler, begin at one end and remove a strip of peel from end to end. Leave a strip of peel about the same width, then peel another strip from end to end. Slice the eggplants about 1/4 inch thick and place in a large bowl of salted water and let them soak for about 30 minutes.

Slice the green pepper into thin rings. Grate 1 large tomato or maybe 2 plum tomatoes.

Cook the onion in 1 tablespoon of olive oil in a large skillet until tender. Then add the bell pepper slices and cook until soft. Then add the ground beef and cook until browned, then add the grated tomato, 1 tablespoon of tomato paste, 1 teaspoon of salt, 1/2 teaspoon of pepper, and the allspice. Mix this together, reduce heat to a simmer, cover and cook for about 10 minutes then remove from heat.

Grate the other 3 large tomatoes or 4-8 plum tomatoes and put them into a small saucepan. Add the remaining 1 tablespoon of tomato paste, 1/2 teaspoon of salt, 1/4 teaspoon of pepper, oregano, and sugar. Simmer this on low heat for about 10 minutes then remove from heat.

Remove the eggplant slices from the water and blot them dry with paper towels. Fry them on both sides in olive oil until tender and golden brown on both sides. Drain them well on paper towels.

Line the bottom of a large baking dish with the fried eggplant slices to make a single layer, make sure there are no gaps between the pieces. Spread the tomato sauce over the eggplant. Next, cover the tomato sauce layer with the meat mixture.

Preheat your oven to 180 C.

In a large pan, melt the butter over medium heat. Whisk in the flour and cook for a minute, then whisk in the milk and continue whisking until the sauce thickens, when it has the consistency of pudding it is ready.

Pour the hot sauce over the meat layer, covering it completely. Sprinkle the grated cheese evenly over the top of the casserole. Bake for 30 minutes or until the top turns golden brown and the casserole is heated through.

Let the casserole rest for at least 10 minutes before cutting and serving.