Place chicken on trivet in boiling water. Cover and steam for 1 hour. Save stock. Cook broccoli slightly, drain, cut into pieces when cool. Save some florets for garnish. Put in bottom of well greased 9 x 13 baking dish. Salt and pepper to taste. Make sauce: Melt butter, add flour. Add water as needed to reserved chicken stock to make 2 cups. Stir into flour and butter, add milk or cream. Cook for 5 minutes. Slice chicken thin and pull apart. Pour 1/3 sauce over broccoli, sprinkle with cheese. Spread sauteed mushrooms, arrange chicken on top. Cover with rest of the sauce, sprinkle thickly with cheese and drizzle top with melted butter. Bake 30 minutes at 350 degrees. Place under broiler until golden brown. Garnish top with broccoli florets.