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