Cook rice with water according to package directions.
Meanwhile, preheat oven to 350 degrees F and coat and 13" x 9" baking dish with non-stick cooking spray.
Add vegetable oil to a large pan or Dutch oven and place over medium-high heat. Add chicken and cook, stirring, until lightly browned and cooked through; season with salt and pepper, to taste. Transfer cooked chicken to a plate and set aside. Add onion, celery, and broccoli to pan and cook, stirring occasionally for several minutes until broccoli is bright green and just slightly softened. Add mushrooms and garlic and saute for another 3 or 4 minutes. Remove from heat.
Melt butter in a medium saucepan over low heat. Add the flour and cook, whisking, for about two minutes. Gradually whisk in the warm milk. Continue to cook, whisking, until thickened. Add seasoning salt and fresh ground pepper and stir to combine. Remove the pan from the heat and add the mozzarella and cheddar cheese, stirring until cheese has melted.
Add the cooked rice, chicken, and cheese sauce to the cooked vegetables in the Dutch oven and stir to combine. Pour mixture into prepared baking dish. Sprinkle with Parmesan and bread crumbs. Cover with foil and bake for 30 minutes. Remove foil and set oven to BROIL and cook for another 2 to 3 minutes until topping is lightly golden brown.