Pour enough water into a fish kettle to cover the fish. Add the celery, carrot, onion, bay leaves, peppercorns and 50ml/2fl oz of the vinegar. Bring to the boil and simmer for 20 minutes to make a court bouillon. Carefully lower the salmon into the court bouillon, increase the heat once more and poach gently for 16-18 minutes.
Warm. Peel the cucumber and slice it as thinly as possible, preferably on a mandoline. Chop the leaves from the remaining mint sprigs and mix with the cucumber, the remaining white wine vinegar and a pinch of salt.
Lift the salmon, still sitting on the trivet, out of the fish kettle, and allow any excess water to drain away. Carefully lift it off the trivet with 2 fish slices and put it on a serving plate. Remove the skin by making a shallow cut through the skin along the backbone and around the back of the head and carefully peeling it back. Carefully turn the fish over and repeat on the other side.
To serve, run a knife down the length of the fish between the 2 fillets and gently ease them apart and away from the bones. Lift portion-sized pieces of the salmon on to each serving plate, then turn the fish over and repeat. Serve with the new potatoes, mayonnaise and cucumber salad.
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