Place the hazelnuts, almonds, pine nuts, anchovies, garlic and capers into a food processor and blend.
Transfer the nut mixture to a bowl. Add the eggs, crushed grissini, mint, parmesan, lemon zest, salt and freshly ground black pepper and stir well to create a paste. If it appears a little wet, add some more crushed grissini.
Place the trout on a chopping board and stuff the cavities with the paste.
Tie each trout in three places with raffia or kitchen string to wrap the fish closed around the stuffing.
Heat the butter in a large frying pan big enough to fit all four trout; alternatively divide the butter between two frying pans.
When the butter has melted, add the fish and fry for 3-5 minutes on each side, or until just cooked through.
Bring a pan of water to the boil over a high heat. Add a pinch of salt and the purple sprouting broccoli and cook for 2-3 minutes. Drain and set aside.
Heat a frying pan until hot and add the olive oil and garlic, stir fry for 30 seconds before adding the drained broccoli. Stir-fry for one minute, then add the lemon juice and season, to taste, with salt and freshly ground black pepper.
To serve, place each trout onto a serving plate and place equal amounts of the broccoli alongside.