In a large saucepan, cook noodles according to package directions until tender.
In another saucepan, melt butter; stir in flour until smooth. Gradually add milk. Bring to a boil; cook and stir for 2 minutes or until thickened. Stir in the spinach, nutmeg, salt and pepper. Drain noodles. Add to spinach mixture; toss gently to coat.
Transfer to a greased shallow 2-qt. baking dish; sprinkle with cheese. Cover and bake at 350° for 20 minutes or until heated through.