• In a large saucepan, melt 4 tablespoons butter; stir in flour until smooth. Gradually add milk and broth. Bring to a boil; cook and stir for 2 minutes or until thickened. Remove from the heat. Stir a small amount of sauce into the eggs; return all to pan, stirring constantly. Cook and stir over low heat until mixture reaches 160°, about 1 minute. Remove from the heat; stir in 1/2 cup Parmesan cheese, 1/2 teaspoon salt, nutmeg and cayenne. Set aside.
• In a large skillet, saute onion and garlic in remaining butter until tender. Add chicken; cook and stir until juices run clear. Stir in the broccoli, carrot and remaining salt. Cover and cook over medium heat for 5 minutes or until vegetables are tender. Add parsley and pepper.
• In a greased 13-in. x 9-in. baking dish, layer 1/2 cup of the sauce, three noodles, half of the chicken mixture, 1/2 cup sauce and a third of the mozzarella cheese. Sprinkle with 1 tablespoon Parmesan cheese. Top with three noodles, the remaining chicken mixture, half of the remaining mozzarella, 1 tablespoon Parmesan and 1/2 cup sauce. Top with the remaining noodles. Place the remaining mozzarella slices over noodles. Top with remaining sauce; gently lift noodles away from sides of the dish, letting sauce flow underneath. Sprinkle with remaining Parmesan.
• Bake, uncovered, at 350° for 45-50 minutes or until bubbly and golden brown. Let stand for 15 minutes before cutting.
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