Preheat the oven to 425 degrees F.
For the fish: Place the trout fillets in an ovenproof dish, drizzle over the honey and soy sauce, and add the ginger. Transfer to the oven and cook until the fish is just cooked through and flakes easily with a fork, 8 to 10 minutes.
Meanwhile, prepare the salad: In a food processor fitted with the shredding disk, shred the apples, carrots, fennel and cabbage. Combine the shredded vegetables with the basil, mint, peanuts and sprouts in a large serving bowl.
For the dressing: In a bowl, whisk together the ginger, lime juice, honey, soy sauce, sesame oil and fish sauce. Adjust to taste.
Pour the dressing over the salad and toss gently, making sure the salad ingredients are well coated.
Remove the fish from the oven, squeeze over the lime juice, and serve with the dressed salad.