Saute onion and celery in butter in a large skillet over medium heat till clear. Add mushrooms and saute till soft.
Add flour to skillet and stir to make a blond colored roux. Slowly add cream and milk, stirring to incorporate well. Using a whisk makes this quicker. Add basil, thyme and parsley and salt & pepper to taste. Cook over medium heat until thickened.
Meanwhile, blanch the broccoli by adding it to a pot of boiling water for no more than 2 minutes. This keeps the bright green color.
In a large bowl, mix broccoli, rice, onion & mushrooms sauce, & cheese. Add chicken broth if mixture seems dry. Season with salt and pepper and Tabasco sauce to taste.
Pour into greased casserole dish. Cover with bread crumbs.
Bake 30-45 minutes at 350 degrees until bubbly all the way through.