Tip the salmon into a food processor with the paste, ginger, soy and chopped coriander. Pulse until roughly minced. Tip out the mix and shape into 4 burgers. Heat the oil in a non-stick frying pan, then fry the burgers for 4-5 mins on each side, turning until crisp and cooked through.
Meanwhile, use a swivel peeler to peel strips of carrot and cucumber into a bowl. Toss with the vinegar and sugar until the sugar has dissolved, then toss through the coriander leaves. Divide the salad between 4 plates. Serve with the burgers and rice.