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 boiling water and cook 2-3 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 20-22 minutes, or until the breadcrumbs are lightly browned and the mixture is bubbly and hot.
Serve over rice, noodles, or mashed potatoes, as desired.