Preheat the Oven: Preheat your oven to 350°F (175°C).
Prepare the Stuffing: Prepare the stuffing mix according to the package instructions and set aside.
Cook Vegetables: In a large skillet, melt the butter over medium heat. Add the chopped celery and onion, cooking until softened, about 5-7 minutes.
Mix Sauces: In a medium mixing bowl, combine the cream of chicken soup, cream of mushroom soup, chicken broth, and milk. Whisk until smooth.
Combine Ingredients: In a large pot, combine the cooked chicken, cooked vegetables, and sauce mixture. Add salt, black pepper, and sage (if using). Stir until everything is well mixed.
Assemble the Casserole: Spread the chicken mixture evenly in a 9x13-inch baking dish. Top with the prepared stuffing mix, spreading it evenly over the chicken mixture.
Bake: Bake in the preheated oven for 30-35 minutes, or until the casserole is hot and bubbly, and the stuffing is golden brown on top.
Serve: Let the casserole cool for a few minutes before serving. Enjoy your comforting Chicken and Dressing Casserole!