Heat oil in a large nonstick skillet over medium-high heat. Sprinkle duck with salt and pepper. Add duck to pan; sauté 5 minutes. Turn and sauté an additional 2 minutes or until desired degree of doneness. Add vinegar; cook 1 minute. Remove from heat; let stand 10 minutes. Cut duck diagonally across grain into thin strips.
Spoon 1/2 cup peas onto each of 4 plates; place 1 breast half on each plate. Drizzle with vinegar sauce; garnish with parsley, if desired.