Put the beef in a non-metallic bowl with the soy sauce, rice vinegar, brown sugar, lime juice and chopped chilli. Leave to marinate for 10 minutes.
Meanwhile, cook the rice according to the instructions on the packet.
Heat the oil in a large frying pan or wok, then add the broccoli, ginger and chilli powder. Stir-fry for 1 minute, then add the carrot ribbons and cook for a further 1 minute. Add the beef with the marinade and the chopped coriander and stir-fry briskly for 1-2 minutes, until the beef is cooked to your liking.
Serve the beef alongside the rice, and garnish with the extra coriander and wedges of lime to squeeze over.