Bring a large saucepan of salted water to the boil, add the potatoes and simmer until tender, about 20 minutes. Drain well, and while still boiling-hot, crush (rather than mash) the potatoes and allow the steam to escape – the drier the mash, the firmer your fish cakes will be.
Leave the mash to cool before stirring in the egg, coriander and green chilli. Generously season with salt and pepper. Set aside.
While the potatoes are cooking, whizz the salmon, ginger and lime zest in a food processor until they form a thick paste.
Peel the outer layer of the lemongrass and discard. Cut the stem in half lengthways and chop as finely as you are able. Add to the salmon paste, then add the salmon mixture to the cooled potato, combining well. Divide the mixture into eight and shape into patties.
Dip each one into the breadcrumbs to coat and put onto a large plate or baking tray. Chill in the fridge for at least an hour to firm up the fishcakes.
Place a large, heavy-based frying pan over a medium heat. Heat the sesame oil and butter together in the pan until beginning to foam, then fry the fish cakes in batches, until golden on both sides.
To make the dipping sauce, combine all the ingredients and pour into a small serving dish. Serve the hot fish cakes with the dipping sauce.