Carefully cut your chicken breasts through the middle (but not all the way through) to create a pocket for your stuffing. Set them aside.
Melt butter in a large skillet on medium heat. Add the chicken, sprinkled with salt and pepper, and cook on each side for about 5 min or until golden brown but not cooked through. Transfer chicken to a baking dish, and set aside.
Add the butter, onion, and mushrooms to the skillet. Cook for about 5 minutes, or until veggies are softened. Preheat oven to 350.
Add the garlic and cook for another minute. Sprinkle with a pinch of salt.
Add the wine and stir to get any bits of the bottom of the pan.
Add the stuffing mix, green onions, and cheese and stir it all together.
Scoop the stuffing mix into the chicken pockets. Get as much in as you can.
Bake the chicken for about 25 - 30 min, or until cooked through. Serve immediately.