Preheat the oven to 350°. Spray a 15x10 casserole dish with cooking spray.
Melt 3 tbsp butter in a large, deep skillet or a dutch oven over medium-high heat. While the butter melts, in a medium sized pot, add broth, rice, greek seasoning, and oil. Mix well and bring to a boil. Cover and reduce heat to low. Cook for 20 minutes. Remove from heat. Add broccoli, re-cover and allow to steam for 3 minutes.
While the rice is cooking, add onion, mushrooms, celery and garlic to the skillet with the melted butter. Saute until soft, 5-6 minutes. Add chicken and remaining seasonings, stirring well. Brown the chicken until it's no longer pink, approximately 5-7 minutes. Drain if there is any excess water or juices.
Add chicken mixture, rice, and broccoli to the casserole dish mixing well and distributing evenly. Add cheese cubes evenly throughout the dish, pushing them down into the rice. Pour country gravy on top. Top with shredded cheese and bake 20 minutes.
While the casserole is baking, melt remaining 2 tbsp butter in a microwave safe dish. Combine the melted butter with the cornflakes.
When the casserole has finished baking, top with the cornflake and butter mixture. Switch the oven to broil and broil for 2-3 minutes or until the cornflake topping is crispy and golden brown. Be careful that it doesn't burn.
Allow to sit 10 minutes and then serve and enjoy!