Place a 9-inch square baking dish next to the stove. Set a large skillet over medium-high heat and add the butter.

While the butter melts, dredge the pork chops on both sides in the flour mixture. Add two pork chops to the skillet.

Sear the pork chops until golden brown, 2-3 minutes on each side. Transfer the pork chops to the baking dish. Repeat with an additional tablespoon of butter and the remaining two pork chops.

Add the butter to the skillet and reduce heat to medium. Once the butter is melted, add the mushrooms and season with the salt and black pepper. Saute the mushrooms until they are shrunken and browned, 4-5 minutes.

Pour the white wine into the skillet to deglaze the pan, scraping up any browned bits on the bottom with a wooden spoon. Allow the mixture to simmer until the liquid is reduced by half, 1-2 minutes. Stir in the cream. Remove from heat.

Pour the mushroom sauce over pork chops. Sprinkle with half the minced scallions, reserving the rest. Top evenly with shredded mozzarella cheese.

Bake the pork chops on middle rack of oven until the cheese is melted and lightly golden, and the pork reaches an internal temperature of 140°F, 9-11 minutes.

Check to see that pork chops are done. Remove from oven or add time as needed.

Sprinkle the reserved minced scallion over the pork chops. Serve immediately.