Place the chicken on a baking sheet fitted with a rack. Sprinkle the chicken all over with salt and pepper. Roast the chicken until it is rich and caramelized and an instant-read thermometer inserted in the thickest part of the leg (avoiding bone) reads 160 degrees F, 30 to 40 minutes. Allow the bird to rest for 20 minutes.
In a mortar and pestle, add the capers, garlic, lemon zest, anchovies, flaky salt and black pepper to taste. Mash into a coarse paste. (You can also use a mini chopper and pulse into a coarse paste, then transfer to a bowl.) Coarsely chop the dill, arugula, basil, parsley and tarragon, if using, together, then add to the anchovy-caper paste. Stir in the oil and set aside.
Cut the chicken into drumsticks and thighs, then halve the breasts (with wings still attached), and arrange on a platter. Spoon the salsa verde over the chicken. Season with some more pepper and smoked salt. Serve.