Heat a small sauté pan over high heat. Salt and pepperduck breast on both sides and sauté, skin side down. When skin is brown, turn over and continue cooking. When done, but still rare, tent with foil and keep warm in a 75°C oven.
Meanwhile, bring vinegar to boil in a sauce pan over high heat. Reduce and add honey. When honey has melted, add stock, ginger, and Thai herbs. Reduce by half. Strain and add rum. Keep warm until ready to use.
Cut duck breast lengthwise into 8 thin slices. Put a few spoonfuls of sauce on each serving plate. Sprinkle mint over sauce. Arrange 4 slices of meat on top of sauce. Sprinkle with sesame seeds and serve.