1Heat oven to 375º. Spray rectangular pan, 11x7x1 1/2 inches, with cooking spray. Cook and drain noodles as directed on package.
2While noodles are cooking, melt butter in 2-quart saucepan over medium heat. Stir in flour and pepper. Cook over medium heat, stirring constantly, until smooth and bubbly; remove from heat. Stir in milk and broth. Heat to boiling, stirring constantly. Boil and stir 1 minute; remove from heat.
3Mix spinach, noodles, half of the sauce, 1/4 cup of the cheese and 1/4 teaspoon nutmeg. Spoon mixture into pan. Place chicken on spinach mixture. Pour remaining sauce over chicken. Sprinkle with remaining 1/4 cup cheese and additional nutmeg.
4Cover and bake 30 minutes. Uncover and bake about 15 minutes longer or until light brown on top and juice of chicken is no longer pink when centers of thickest pieces are cut.