1) Butterfly chicken breasts and set aside. In a food processor, combine the dill and parsley and pulse until finely chopped. Reserve 1/4 cup of the herb mixture for spread, set aside.
2) In a plastic bag set in a medium bowl, combine the remaining herb mixture, half the lemon juice, 4 tablespoons olive oil, and salt and pepper, to taste. Place chicken in the plastic bag, seal and massage to distribute marinade evenly on the chicken. Refrigerate 1 hour, flipping once halfway through.
3) Meanwhile, to make the herb spread, in a small bowl mix together remaining herb mixture, remaining lemon juice, lemon zest, sour cream, mayonnaise, pepperoncini, and salt and pepper, to taste.
4) Preheat griddle to medium high. Remove chicken from bag, being careful not to remove herbs. Season with salt and pepper and cook on griddle, turning once, until juices run clear, approximately 6 minutes on each side. Remove to a cutting board and cut each breast in half.
5) To assemble the sandwich, cut ciabatta pieces in half horizontally, slather one side of bread with dill-pepperoncini spread. Place chicken on other slice, top with baby greens and finish with the piece of bread covered with dill-pepperoncini sauce.