Heat a large skillet or wok over medium-high heat. Add butter and oil until butter melts and starts to froth. Add minced garlic and chopped onion.
Add the zucchini, carrots, broccoli, and mushrooms to the skillet. Stir for about 1 minute, then pour in the soy sauce and teriyaki sauce. Season with salt and pepper.
Transfer the vegetables to a serving dish. If using, sprinkle with sesame seeds. Serve hot, either on their own or alongside hibachi rice or noodles.