Combine rub ingredients in a small bowl. Dress chicken with EVOO, salt and pepper; coat chicken all over with rub and cover. Let stand 1 hour.
Cook chicken in a hot cast-iron pan or outdoor grill over medium-high heat.
Rub the inside of the salad bowl with the split garlic clove. In the salad bowl, whisk tahini with water to loosen then add egg yolk if using, lemon juice, Worcestershire, anchovy paste, pepper, EVOO and cheese, if using.
Add lettuce to the bowl and toss to combine. Add pita chips or croutons, and top with sliced grilled chicken.