Rub duck breast halves with olive oil; sprinkle with 1 tablespoon pepper. Cover and chill 8 hours.
Heat peanut oil in a skillet over high heat. Sprinkle duck with salt; cook 2 minutes, turning once. Reduce heat to medium; cover and cook 20 minutes or until done, turning once. Slice and keep warm.
Core cabbage, and cut into 3/4-inch slices.
Melt butter or margarine in skillet over medium-high heat, stirring to loosen browned particles. Add cabbage; cook, without stirring, 2 to 3 minutes. Cook, stirring constantly, 2 minutes or until tender. Sprinkle evenly with 1/2 teaspoon pepper; serve with duck.