Authentic Greek Moussaka

Name: Authentic Greek Moussaka
Ingredients: 4 medium eggplants, cut lengthwise into 1/3-inch slices; salt to taste; 4 cups milk; 1 stick butter; 6 tablespoons all-purpose flour; 3 large egg yolks, beaten; 7 tablespoons olive oil, divided; 2 medium onions, grated; 3 cloves garlic, finely chopped; 1 pound lean ground beef; 0.5 teaspoon ground allspice; 0.5 teaspoon white sugar; 1 pinch ground cinnamon; salt and ground black pepper to taste; 1 (14 ounce) can tomato sauce; 4 tablespoons chopped fresh parsley; 1 large egg white, lightly beaten; 1.5 cups freshly grated Parmesan cheese