To prepare filling, cook pasta according to package directions, omitting salt and fat. Rinse with cold water; set aside.
Cook beef, onion, and garlic in a large nonstick skillet over medium-high heat until browned; stir to crumble. Add wine, tomato sauce, 1/2 teaspoon salt, nutmeg, and pepper; bring to a boil. Reduce heat; simmer 10 minutes or until thick.
Preheat oven to 350°.
To prepare white sauce, place flour and 1/2 teaspoon salt in a medium saucepan over medium heat. Gradually add milk, stirring constantly with a whisk until blended; bring to a boil. Reduce heat; simmer 10 minutes or until slightly thick, stirring constantly. Remove from heat; set aside. Combine eggs and egg whites in a large bowl. Gradually add hot milk mixture to egg mixture, stirring constantly with a whisk. Stir in 1 tablespoon kasseri cheese until blended.
Spread 1 cup beef mixture in bottom of a 13 x 9-inch baking dish coated with cooking spray. Arrange half of pasta over beef mixture. Top with 1 1/2 cups beef mixture. Repeat layers with remaining pasta and beef mixture. Top with white sauce. Sprinkle with 4 tablespoons kasseri and Romano cheese. Bake at 350° for 30 minutes. Let stand 15 minutes before serving.