*Thicker chops may be cut in half lengthwise to about 1/4-inch thickness.
Heat 2 tbs of the butter in a large skillet. Saute the mushrooms until they begin to caramelize; about 5 minutes.
Remove mushrooms and set aside.
Lightly grease a 13 x 9-inch baking dish.
Melt 1 tbs of the butter in the same skillet.
Dredge pork chops in flour.
Brown half of the pork chops well on both sides.
Add the remaining 1 tbs butter and brown remaining chops.
Place chops in prepared baking dish. Distribute mushrooms over the top.
In the same pan you browned the chops in, add the wine and stock, scraping up all the browned bits from the bottom of the pan. Add salt and pepper to taste.
Bring wine/stock mixture to a boil, then reduce heat to low and simmer for 10 minutes
Preheat oven to 450 degrees F.
Pour wine/stock mixture over the chops and mushrooms.
Mix the shredded cheese with the green onions and distribute evenly across chops and mushrooms.
Bake for 15-20 minutes, or until cheese is melted.