Cook broccoli, 5 minutes, drain and set aside. Saute mushrooms and onion in 2 tablespoons butter until onion is tender; set aside.
Melt 2 tablespoons butter in a heavy saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk; cook over medium heat, stirring constantly, until thickened and bubbly. Remove from heat. Add salt, pepper and cheese; stir until cheese melts. Stir in mushroom mixture.
Place broccoli in a lightly greased 1 1/2 quart casserole. Top with sauce, and bake at 350 for 25 minutes. Serve over rice; sprinkle with soy sauce.