Preheat oven to 350.
Spray a 9x13 baking dish with cooking spray.
In a skillet over medium heat, melt butter.
Add chopped onion and celery.
Sauté veggies about 8-10 minutes until veggies are tender.
Season lightly with salt and pepper.
Spread the veggie mixture evenly into prepared baking dish.
Spread the chicken evenly over top of the vegetables.
In a mixing bowl, combine self-rising flour with half-and-half (or milk).
Pour flour mixture over top of chicken layer.
Do not stir mixture.
In a separate bowl, combine chicken broth and cream of chicken and mushroom soup with a whisk until smooth.
Pour soup mixture over the flour mixture.
Do not mix the layers.
Sprinkle salt and pepper over top of casserole.
Bake for about 60-75 minutes or until the casserole is set.
Sprinkle with fresh parsley for garnish.