Preheat an outdoor grill, indoor griddle or grill pan to medium-high heat. In a bowl, whisk together the EVOO, garlic, basil, thyme, and the zest and juice of 2 lemons. Stir in the chile pepper and parsley; season with salt and pepper. Spoon 3 tbsp. of the dressing into a small bowl and stir in the tahini, vinegar and the juice of the remaining lemon; set aside this sesame sauce for dressing the subs (if its too thick for drizzling, thin with a little water).
Toss the chicken in the remaining marinade to coat well. Thread onto metal skewers or string onto grill wire. Grill, turning occasionally, until cooked through, about 10 minutes.
Pile the lettuce on the rolls and top with the chicken, lots of sesame sauce and the giardiniera.