Slice carrots diagonally. Add basil and cook in salted water until tender. Drain.
Saute onion in butter. Mix flour, salt, mustard, pepper and milk; add to onion and cook, stirring constantly, over medium heat until thick.
Place a layer of carrots in a casserole. Cover with grated cheese. Alternate layers of carrots and cheese until ail used. Pour sauce over top. Sprinkle with croutons. Bake at 350 degrees 15 minutes.