For the teriyaki sauce, mix the ingredients together in a bowl and set aside. The sauce can be used immediately or refrigerated for later use.
Slice the steak into thin strips. Put the steak strips in the teriyaki sauce to coat them then remove and pat dry (you can marinate these for longer if desired or use immediately).
Meanwhile heat a little of the oil in a frying pan and fry the mushrooms, tomatoes and sugar snap peas for 2 minutes, until they are cooked through but still crisp. Add 2 tablespoons of teriyaki sauce, the coriander and mint then cook for a further minute. Remove from the pan and keep warm.
Wipe the frying pan with a paper towel and add a little more oil. Fry the steaks over a medium heat for 2 minutes until slightly browned then turn gently and brown the other side. Be careful not to overcook the beef.
Drain off any excess oil from the pan and discard. Pour a little teriyaki sauce over the beef and continue to cook for a couple of minutes, turning and basting the steaks so that they are well coated and glazed. Add the beansprouts and fry for a further 30 seconds.
To serve, remove the beef from the pan and place on individual plates. Simmer the remaining teriyaki sauce until it is thick and syrupy; be careful not to over-reduce it as it burns easily. Spoon the sauce over the beef and serve immediately with rice.