For the dressing: Whisk together the oil, lemon juice, sesame seeds, oregano and Aleppo-style pepper in a small bowl. Season with salt and pepper.
For the salad: Combine the pita chips, chickpeas, lettuce, tomatoes, cucumbers and onions in a large bowl. Add the dressing and toss well. Let stand while you grill the cheese.
Prepare a grill or grill pan for medium-high heat. Clean and lightly oil the grill grates.
Brush the halloumi with oil and grill, turning once or twice, until lightly charred on the outside and just softened, about 4 minutes total. Transfer to a plate.
Fold the herbs into the salad and season to taste with more salt and pepper if desired. Transfer the salad to plates or a platter. Top with the grilled halloumi and serve.