In a medium saucepan, melt the butter over medium heat and stir in the flour. Cook the flour mixture until it becomes a deep golden brown.
Slowly whisk in the chicken broth cooking until the mixture begins to thicken. Whisk in the half and half, sherry, lemon zest and juice. Remove from the heat. Stir in the salt and pepper until smooth.
Place broccoli in an ungreased 13-in. x 9-in. baking dish. Cover with the rice and then half of the sauce. Top with chicken. Stir the shredded cheese into remaining sauce until smooth. Pour the sauce mixture over the chicken.
Melt the remaining butter and toss with the bread crumbs. Sprinkle over the casserole. Bake, uncovered, at 350° for 35-45 minutes or until golden brown and bubbling.