Heat a large nonstick skillet over medium-high heat. Add the first 4 ingredients, and sauté 5 minutes. Add the wine and next 6 ingredients (wine through tomatoes). Bring mixture to a boil; reduce heat, and simmer 10 minutes or until thick.
Combine the flour, milk, and 1/4 teaspoon nutmeg in a medium sauce-pan, and bring to a boil. Reduce heat, and cook for 7 minutes or until thick, stirring constantly. Remove milk mixture from heat. Stir in feta cheese, 1 tablespoon Parmesan cheese, and egg.
Sprinkle 1 tablespoon breadcrumbs in a 2-quart casserole coated with cooking spray. Place 2 cups spaghetti in casserole, and top with 2 cups beef mixture and 1 cup sauce. Repeat layers. Combine 1 tablespoon Parmesan cheese and 1 tablespoon breadcrumbs, and sprinkle over the casserole. Bake casserole at 375° for 30 minutes or until golden brown. Let stand for 5 minutes. Garnish with fresh oregano, if desired.