Peel and roughly chop the garlic. Peel and slice the ginger. Rinse and halve the chilli. Flick out the seeds and white bits. Finely chop it. Finely slice the lime leaves. Grate or pare the zest from the lime. Juice it.
Pop the garlic, ginger, chilli, lime leaves, lime zest and half the lime juice into a small food processor or blender. Add 2 tbsp olive oil. Blitz to make a rough paste. If you don't have a processor or blender, finely chop everything and stir together.
Tip the marinade into a non-metallic bowl. Add the beef stir-fry strips. Season. Stir to mix. Leave for 10 minas to marinate.
Peel and thinly slice the onion. Rinse the pepper and halve it. Scoop out the seeds and white bits. Slice thinly. Break the broccoli into small florets. Rinse them. Put to one side. Fill the kettle and boil it.
Tip the rice into a small pan. Pour in 250ml hot water from the kettle. Cover. Bring to the boil. Turn the heat right down. Simmer for 6 mins till all the water has been absorbed. Take off the heat. Steam, lid on, for 2-4 mins till cooked.
Warm a deep frying pan or wok. Lift the beef out of the marinade. Add to the wok (but keep the marinade). Stir-fry for 5 mins over a high heat till browned. Lift the beef out of the pan. Pop on a plate.
Add the onion, pepper and broccoli to the pan. Stir-fry for 4-5 mins till starting to soften. Stir in any leftover marinade.
Pour in the coconut milk and the rest of the lime juice. Slide the beef back into the pan. Simmer for 3-5 mins till everything is tender. Add a splash of hot water if it looks too dry. Taste and adjust the seasoning. Serve the beef with the rice.