Cook florets in 1 inch boiling salted water 3 to 5 minutes; drain.
Arrange broccoli in greased 9-inch square pan.
Melt 5 tablespoons butter and blend in flour, salt and pepper; cook and stir until smooth.
Remove from heat and stir in milk; bring to boil and boil 1 minute, stirring constantly. Add cheese and remove from heat. Saute mushrooms in remaining 1 tablespoon butter until tender and add to sauce; add green pepper and cook 1 minute.
Pour sauce over broccoli; sprinkle with additional cheese and paprika, if desired.