In heavy skillet over high heat, toss walnuts until they just begin to brown, about 3 minutes. Transfer nuts to a small bowl. Add oil and heat over high heat. Brown chops about 1 minute on each side. Cover pan, reduce heat to low and cook chops 6 minutes, just until cooked through. While chops cook, combine cheese, green onions, and pepper with nuts and mix well. Transfer chops to a platter and return pan to the stove. Pour in water; bring to a boil, scraping up brown bits on bottom of pan. Cook until juices thicken slightly. Pour juice over chops and top with nut mixture.