How to Make It
Prepare the Radishes: Remove the greens. Trim Radishes, and set aside. Discard any tough stems from greens. Rinse greens, and blot dry. Set aside 1/2 cup lightly packed greens for Pesto, and set aside 1/4 cup lightly packed greens for Salad. (Discard any remaining greens, or reserve for another use.)
Prepare the Pesto: Pulse together Parmesan, almonds, garlic, lemon zest and juice, salt, and pepper in a food processor until finely chopped, 7 to 8 times. Add mint leaves and reserved 1/2 cup radish greens; pulse until finely chopped, 6 to 7 times. Add oil; pulse until mixture forms a loose paste with a bit of texture, 6 to 7 times. Store, tightly covered, in refrigerator up to 1 week.
Prepare the Salad: Preheat oven to 375°F. Halve any radishes or potatoes that are larger than a golf ball; leave the rest whole. Place on a rimmed baking sheet. Add garlic; drizzle with oil, and sprinkle with salt and pepper. Toss to coat; spread mixture in a single layer. Roast in preheated oven until vegetables are tender and browned in spots, about 30 minutes.
Divide roasted vegetable mixture evenly among 4 plates; top with trout, Parmesan, mint leaves, and reserved 1/4 cup radish greens. Sprinkle with shallot and lemon peel strips. Top each Salad with 2 tablespoons Pesto. Serve immediately.