1. Heat a large nonstick skillet over medium-high heat. Add oil to pan; swirl to coat. Sprinkle duck with 1/2 teaspoon salt and 1/4 teaspoon pepper. Add duck to pan; cook 3 minutes or until browned. Turn duck over; cook 3 minutes or until desired degree of doneness. Remove duck from pan; let stand 5 minutes.
2. Add blackberries, shallots, and thyme to pan; sauté 2 minutes or until slightly softened. Add port; cook 1 minute or until syrupy. Add stock and any juices from duck; cook 5 minutes or until thickened and reduced to about 1/2 cup. Stir in remaining 1/4 teaspoon salt, remaining 1/4 teaspoon pepper, and vinegar. Cut duck across grain into thin slices; serve with sauce.
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