Place the haddock pieces onto a plate and drizzle with the juice of one of the limes and toss to evenly coat.
Place the remaining ingredients, except the oil, into a small food processor and blend to a paste.
Spread the paste over the haddock pieces.
Heat enough vegetable oil to just coat the bottom of a frying pan, add the haddock and fry on all sides for 2-3 minutes, until golden-brown and just cooked through.
For the broccoli, heat a wok until hot, then add the vegetable oil and mustard seeds and cook for 30 seconds, or until the seeds start to pop.
Add the broccoli, water and garlic and stir-fry for 3-4 minutes, or until the broccoli is tender.
Add the chilli oil and season, to taste, with salt and freshly ground black pepper.
To serve, place equal portions of the haddock onto each plate and place a spoonful of the broccoli alongside.