Heat 2 tablespoons oil in heavy large skillet over medium-high heat.
Add cabbage, mushrooms, bok choy, carrot and green onions and stir-fry until vegetables are crisp-tender, about 3 minutes.
Add 3 tablespoons oyster sauce and 3 tablespoons soy sauce; stir 1 minute to blend flavors.
Season to taste with salt and pepper.
Transfer vegetable mixture to medium bowl.
To same skillet (do not clean) add the broth, 1/2 tablespoon oil, remaining 3 tablespoons oyster sauce, remaining 1/2 tablespoon soy sauce, butter and vinegar.
Boil until sauce thickens, whisking occasionally, about 3 minutes.
Season with salt and pepper.
Keep warm.
Sprinkle tuna with salt and pepper.
Heat remaining 3 tablespoons oil in another large skillet over high heat.
Add 3 tuna steaks and cook to desired doneness, about 2 minutes per side for medium-rare.
Transfer to small baking sheet.
Repeat with remaining tuna.
Divide vegetables among 6 plates.
Top with tuna.
Ladle sauce around tuna.
Sprinkle with sesame seeds, if desired.