Arrange eggplant slices on paper towels; sprinkle both sides with salt. Let sit for 30 minutes to draw out moisture. Pat dry with paper towels.
Brush each side of the eggplant slices with olive oil. Bake at 400°F until browned and slightly crisp, about 20 minutes, flipping halfway through.
Sauté onions and garlic in a pan until translucent. Add ground beef, breaking it up until browned. Stir in crushed tomatoes, wine, oregano, cinnamon, black pepper, and simmer for 20 minutes until thickened. Adjust seasonings as needed.
Melt butter in a saucepan. Stir in flour and cook for 1 minute. Gradually whisk in 2 1/2 cups milk, and continue to cook until the sauce thickens. Add up to 1/2 cup more milk if needed to thin the sauce.
Remove from heat, stir in nutmeg, and gradually whisk in beaten eggs until smooth. Fold in 1 cup of Parmesan cheese.
In a baking dish, layer eggplant, meat sauce, and repeat. Pour béchamel sauce over the top layer, and sprinkle with remaining 1/2 cup of Parmesan cheese.
Bake at 350°F for 45-55 minutes or until the top is golden and bubbly. Let rest for 10 minutes before serving. Garnish with fresh parsley.