Preheat the oven to 350 F. In a small pot, bring water and butter to a boil. Once boiling, add the packet of stuffing and stir. Remove from heat, put the lid on for 5 minutes, and fluff with a fork.
In a medium-sized skillet, heat the olive oil and saute the onion, celery, and bell pepper.
Place shredded chicken in the bottom of a 9 x 9-inch casserole dish
Sprinkle the sauteed veggies and broccoli florets on top of the chicken
In a small bowl, mix the cream of chicken soup, cream of mushroom soup, and sour cream. Pour this mixture carefully on top of the veggies
Spoon the stuffing on top and bake for 45 mins or until brown and bubbly