Preheat oven to 375°F (190°C). Grease a 9 x 13-inch baking dish with nonstick cooking spray.
In the prepared baking dish, combine mushrooms, green onions, coleslaw mix, carrots, and uncooked rice. Toss gently so that everything is evenly distributed throughout the pan.
In a large bowl or measuring cup, whisk together chicken broth, soy sauce, brown sugar, hoisin sauce, sesame oil, rice vinegar, garlic, and ginger. Pour evenly over the ingredients in the baking dish.
Cover the dish tightly with foil. Bake for 50 minutes. Uncover the dish and use a fork to fluff the rice. At this point, the rice should be almost tender. If the rice is still crunchy, cover and return it to the oven for 5-10 more minutes, or until the rice is just about done. Taste and season with salt and pepper, if desired.
Stir in the cooked chicken. Return the dish to the oven, uncovered, and bake for 5 more minutes, or until the chicken or pork is warmed through, and the rice is completely tender.
Top with chow mein noodles and garnish with extra sliced green onion, if desired.