Preheat oven to 350 degrees F (175 degrees C). Lightly grease a baking dish.
Stir the chicken broth, mushroom soup mix, mustard, and honey together in a bowl until thoroughly blended. Set aside.
Spread the rice evenly over the bottom of the prepared baking dish. Cover the rice with a layer of ham, then the chicken.
Heat the olive oil in a large skillet over medium heat. Stir in the onion, garlic, celery, and carrots; cook until onion is transparent and caramelized, about 5 minutes. Stir in the tomatoes, and cook 5 minutes more. Spoon the vegetables evenly over the chicken in the baking dish. Deglaze the skillet by adding the Marsala wine; cook and stir over medium heat to loosen any browned pieces of vegetables from the bottom. Let the liquid cool slightly, then stir into the chicken broth mixture. Pour the chicken broth mixture over the vegetables in the baking dish. Sprinkle with parsley, bay leaf, basil, cayenne pepper, and thyme. Cover the baking dish with foil.
Bake the casserole in preheated oven until top bubbles, about 50 minutes. Remove the foil, and stir in the sour cream. Sprinkle mozzarella cheese and bread crumbs evenly over the top. Bake, uncovered, 10 minutes more.
