Preheat the oven to 350°F (175°C).
In a large saucepan, combine the uncooked rice, chicken broth, salt, black pepper, garlic powder, and onion powder. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes until the rice is partially cooked.
While the rice is cooking, melt the butter in a medium saucepan over medium heat.
Whisk in the flour and cook for 1-2 minutes until lightly golden, stirring constantly.
Gradually whisk in the milk and continue cooking until the sauce thickens, about 5 minutes.
Remove from heat and stir in the sour cream, 1 cup of cheddar cheese, 1/2 cup Monterey Jack cheese, paprika, and cayenne pepper until smooth.
In a large mixing bowl, combine the partially cooked rice, cheese sauce, chopped onion, celery, and green bell pepper. Mix well.
Lightly grease a 9×13 inch casserole dish.
Place the chicken breasts in the casserole dish and season them lightly with salt and pepper.
Pour the rice and cheese mixture evenly over the chicken breasts, covering them completely.
Sprinkle the remaining 1 cup cheddar cheese and 1/2 cup Monterey Jack cheese on top.
Cover the casserole dish tightly with aluminum foil.
Bake in the preheated oven for 45 minutes.
Remove the foil and continue baking for an additional 15 minutes, or until the chicken is cooked through and the cheese is bubbly and golden.
Remove from the oven and let it rest for 5 minutes.
Sprinkle chopped fresh parsley over the top before serving.