Preheat the oven to gas 7, 220° C, fan 200° C. Heat two medium pans of water.
In a large frying pan, melt the butter over a low heat and sweat the carrot, leek and tarragon in one-third of the butter for 1 minute. Season with salt and pepper, then leave to cool.
Put the trout fillets in pairs on pieces of oiled nonstick baking paper large enough to wrap them in. Season the fish with salt and pepper, then spoon half the lemon juice and white wine over each pair. Dot the fish with half the remaining butter. Sandwich half the vegetable filling between each pair of fillets and wrap them up in the paper to make two papillotes (parcels).
Bake the papillotes on a baking sheet in the preheated oven for 12 minutes.
While they are in the oven, cook the potatoes and beans in the pans of boiling water.
Serve the parcels immediately on two warmed plates with the drained potatoes and the green beans tossed in the remaining butter. Allow the diners to open their own papillotes so that they get the full benefit of the aromas that rise from them.
*Inspired by Victoria A. featured in the Realfood Cookbook