1. Sprinkle eggplant with 2 teaspoons of salt and place a layer of paper towels on top of the salted slices. Place a heavy casserole or bowl on top of eggplant, pressing down to squeeze out excess water. Arrange half of the eggplant slices in a 13x9x2-inch baking dish.
2. In a large skillet, brown ground beef; drain off excess fat. Add drained tomatoes, breaking up with a spoon. Add garlic powder, salt, pepper, oregano, and cinnamon. Simmer for 5 minutes, stirring occasionally. Spread meat mixture over the eggplant. Top meat mixture with remaining eggplant slices.
3. In a medium saucepan, melt butter. Stir in flour; remove from heat. Gradually stir in milk; return to heat and cook until thickened, stirring constantly. Add shredded cheese and continue stirring until cheese is melted and sauce is smooth. Add a small portion of the mixture to the eggs, beating quickly, then return egg mixture to sauce in saucepan, whisking in quickly. Pour cheese sauce over the all.
4. Bake at 400 degrees for 30 minutes, or until topping is set. Let stand 5 minutes before serving.