Eggplant Moussaka {Greek Lasagna}

Ingredients

• 3 large eggplants (sliced lengthwise into ¼-inch thick slices)
• Salt and pepper (to taste)
• Olive oil (for brushing)
• ½ cup shredded parmesan cheese
• 1 tablespoon olive oil
• 1 large onion (chopped)
• 1 pound ground beef
• 2 garlic cloves (minced)
• 2 teaspoons oregano
• 1 teaspoon cinnamon
• ½ teaspoon salt
• ½ teaspoon black pepper
• 1 15- ounce canned diced tomatoes ( with juices)
• 4 tablespoons butter
• ¼ cup all-purpose flour
• 2 ½ cups milk (warmed)
• ¼ teaspoon nutmeg
• 2 eggs