Combine the pickled pepper juice with the olive oil, garlic, lemon zest, chili flakes, cumin, coriander, onion, thyme, sesame seeds, salt and pepper. Turn the chicken in the marinade and let stand for about 15-20 minutes while you pre-heat the grill, griddle pan or outdoor grill to medium-high heat.
Dress the broccoli with olive oil, salt and pepper and roast in a 450°F oven or grill on outdoor grill until the stalks are tender-crisp and florets are crispy at the edges.
Grill the chicken for about 8 minutes or until cooked through; thinly slice and douse with lemon juice.
In a small bowl, combine the tahini with water, lemon juice, garlic, cumin and salt, and adjust the seasoning, to taste.
Char the breads in a hot skillet or on a clean grill or griddle. Fill the pitas with the broccoli, sliced chicken, tahini, tomatoes, onions and hot peppers.