Season the carp fillets with salt and pepper. Poach in simmering water for 8-10 minutes or grill over medium heat for 4-5 minutes per side until the fish flakes easily with a fork.
Allow the cooked carp to cool slightly, then gently flake it into bite-sized pieces, removing any small bones.
In a large mixing bowl, combine the mixed greens, cucumber, radish, and carrot. Add red onion, cherry tomatoes, and capers if using.
In a small bowl, whisk together the olive oil, lemon juice, chopped dill, salt, and pepper. Add honey, Dijon mustard, and minced garlic if using.
Add the flaked carp to the vegetable mixture, distributing it evenly throughout the salad.
Drizzle the prepared dressing over the salad ingredients, starting with about half the amount and adding more to taste.
Gently toss all ingredients together, being careful not to break up the fish too much.
Taste and adjust seasonings as needed, then serve immediately on chilled plates.
