For the potatoes, in a pan of lightly salted boiling water simmer the potatoes for 7-10 minutes, or until tender. Drain and cut each potato in half. Dress the warm potatoes with the remaining ingredients. Season, to taste, with salt and freshly ground black pepper.
For the trout, pat the trouts dry to remove any excess moisture and season with the salt and pepper.
Melt the butter in a large ovenproof frying pan over a medium heat until foaming, then add the fish and fry for 5-6 minutes on each sides. Remove the fish from the frying pan and set aside on a warm plate.
For the sauce, add 40ml/3 tbsp water to the hot frying pan so that the caramelised juices are dissolved and emulsified into the liquid as it boils. Add the remaining ingredients to the frying pan and return to the boil. Season to taste with salt and freshly ground black pepper.
To serve, place the fish on large oval serving plates and pour the sauce over and around the fish. Sprinkle the chopped parsley over the top and serve. Serve the dressed potatoes in a side bowl.