In a large skillet, heat the olive oil over medium heat. Add the chopped onion and garlic, sautéing until softened, about 3 minutes.
Stir in the diced carrots and celery; cook for another 5 minutes until tender.
In a large mixing bowl, combine the cooked rice, shredded chicken, steamed broccoli, cooked vegetable mixture, chicken broth, cream of mushroom soup, dried thyme, paprika, salt, and pepper. Mix until everything is well incorporated.
Transfer the mixture into a greased 9x13 inch baking dish, spreading it evenly.
Sprinkle the cheddar cheese on top of the casserole.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
Remove the foil and bake for an additional 15-20 minutes, or until the cheese is bubbly and slightly golden.
Once baked, let it sit for 5 minutes before serving. Garnish with fresh parsley if desired.