Melt the 2 Tbsp. butter in a skillet set over medium heat. Add the onion, celery and apple and cook until tender, about 5 minutes. Place in a bowl and cool to room temperature. Mix in remaining ingredients, except chicken and 1 Tbsp. butter.
Preheat the oven to 350°F.
Place the chicken in a roasting pan. Loosely fill the main cavity of the chicken and the cavity behind the flap of skin at the neck end. Fold the wings under the body. Loosely tie the legs together. Put some more stuffing at the point where the legs meet. (See Note below on how to handle leftover stuffing.) Brush the chicken with the 1 Tbsp. melted butter; season with salt and pepper.
Roast the chicken 1 hour 45 minutes, basting occasionally, or until the temperature in the deepest part of the chicken thigh registers 185°F on an instant read meat thermometer.
After stuffing the chicken, place the leftover stuffing in a lightly buttered baking dish. Cover and bake alongside the chicken 20 minutes. Uncover and bake 10 minutes more, or until hot.