Boil chicken in seasoned water until tender. Save broth. Bone the chicken in large pieces, then slice.
Cook broccoli until just tender, drain, and place in casserole dish.
Melt butter in top of a double boiler and blend in the flour. Measure the chicken broth. If there is not enough to make 2 cups, add milk to make up the difference. Add the broth to the butter and flour, stirring until thickened. Add salt, pepper and sherry.
Cover the broccoli in the casserole dish with a layer of chicken, then add the sauce. Sprinkle with grated cheese. Bake in 400 degree oven for about 12 minutes.