Carefully cut your chicken breasts through the middle, but not all the way, to create a pocket for your stuffing. If it doesn't stay all the way closed, and there are holes in it...it will be okay. Set them aside.
Melt butter in a large skillet on medium heat. Add the chicken, sprinkle with salt and pepper, and cook on each side for about 5 min or until golden brown. It won't be cooked through, but that's okay. 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 off the bottom of the pan.
Add the stuffing mix, green onions, and cheese and stir it together.
Scoop the stuffing mix into the chicken pockets. Get as much in as you can.
Bake the chicken for 25 - 30 minutes or until cooked. Serve immediately, or it can be refrigerated or frozen until later -- it reheats well! (I made a bunch and portioned it out for meals later.)