Combine fresh ginger, 1/4 teaspoon salt, and 1/8 teaspoon pepper. Cut pork crosswise into 8 pieces; rub pork with ginger mixture. Let stand 15 minutes.
Heat oil in a large nonstick skillet over medium heat. Add shallots; cook 5 minutes or until tender, stirring frequently. Stir in remaining 1/4 teaspoon salt, 1/8 teaspoon pepper, plums, sugar, and ground ginger. Cook 8 minutes or until plums are tender; stir in wine and vinegar. Reduce heat; simmer 10 minutes. Add butter; stir until butter melts.
Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add pork to pan; cook 3 minutes on each side or until desired degree of doneness. Serve sauce over the pork. Sprinkle with walnuts.