Lay pork chops flat onto your work surface. Use the tip of a sharp boning or paring knife to cut a pocket in each pork chop making a 2 inch slit in the side.
Mix mushrooms, Swiss cheese, parsley, garlic powder, black pepper, and salt in a bowl; stuff pork chops with mushroom mixture. Secure the open side with a toothpick.
Whisk eggs in a bowl; pour bread crumbs into a separate bowl. Dip the stuffed pork chops into the beaten egg; press pork chops into bread crumbs until completely coated.
Heat oil in a skillet over medium heat; place pork chops, pocket side-down, into the hot oil. Cook until outside of pork chops is browned, 2 to 3 minutes per side.
Pour in enough wine to come halfway up pork chops. Reduce heat to low, cover skillet, and simmer until pork chops are tender, about 2 hours. Check wine level occasionally and add more as needed. An instant-read thermometer inserted into the center should read 145 degrees F (63 degrees C).