Preheat oven to 400°F. Grease a 9x13 baking dish (or a 3 quart casserole dish).
If using raw chicken breasts, in a large skillet, heat olive oil on medium high. Add the chicken pieces and cook until cooked through, about 10 minutes. Set aside.
Meanwhile, place broccoli in a large pot of boiling water and cook 2 to 3 minutes or just until tender crisp. Drain well and put in the bottom of the baking dish.
Meanwhile, in a large bowl, combine 1 cup cheddar cheese, soup, sour cream, milk, and seasonings. Stir in chicken and spread on top of broccoli in baking or casserole dish. Sprinkle with remaining cheese.
In a small bowl, mix bread crumbs and butter. Sprinkle over the cheese.
Bake 20 to 22 minutes, or until the breadcrumbs are lightly browned and the mixture is bubbly and hot.
Serve over rice, noodles, or mashed potatoes, as desired.