Peel and chop your ginger and turmeric. Remove the tough outer layers of the lemon grass and roughly chop the stem. Halve the chilli. Set aside one half.
Pick off the coriander leaves and place the stalks in a food processor with the ginger, turmeric and half the chilli. Blitz to a paste then put in a bowl. Finely chop if you don't have a processor.
Roughly chop the broccoli florets and place them in the food processor. Pulse a few times till you have a 'rice'. Grate or finely chop the broccoli if you don't have a processor. Zest the lime.
Cut the pak choi in half. Add ½ tbsp olive oil to the pan and fry the pak choi, cut side down, for 2-3 mins till charred. Remove from the pan. Cut the carrots in half lengthwise, or quarters if they're large. Finely chop a handful of the carrot leaves.
Heat 1 tbsp olive oil in the pan. Add the paste and cook for 2 mins till aromatic. Pour in the coconut milk and 100ml boiling water. Bring up to a simmer then add the carrots . Cook for 10-15 mins till just tender.
In a large frying pan or wok tip in the broccoli rice with 1 tbsp hot water and half of the carrot leaves. Cook for 3 mins then add the lime zest, half of the coriander leaves and season.
Place the charred pak choi and remaining carrot leaves into the coconut broth for 1 min to warm through. Squeeze in the juice of the lime. Serve with the broccoli rice. Scatter with coriander leaves and slices of the remaining chilli.