For the sheet pan roast chicken and spring vegetables:
Preheat oven to 400ºF (200ºC).
Remove backbone from chicken and discard. Break the chicken down into 10 parts by separating the wings, the thighs, the legs and the breasts (each halved).
Arrange the chicken, carrots, potatoes, radishes, asparagus and lemon slices in a single layer on a baking sheet. Slide your fingers under the skin of the chicken and push the butter under the skin. Drizzle the olive oil over and season the vegetables and chicken with salt and pepper.
Roast until the chicken is cooked through and the skin is crisp and golden brown, about 40 minutes.
For the carrot top and walnut pesto:
Heat a small sauté pan over medium-low heat, add the walnuts and toast until they are fragrant and just begin to brown, about 3 minutes. Remove from the pan and set aside.
Add the walnuts, carrot tops, parsley, shallot, garlic and olive oil to a blender and pulse until combined. Remove to a small-mixing bowl and stir in the lemon zest, lemon juice and Pecorino Romano. Season to taste with salt and set aside.
For serving:
Divide the vegetables and chicken among plates and top with carrot top walnut pesto.