Preheat a grill or grill pan until hot. Brush the eggplant slices with EVOO, place on the grill and cook, turning once, for 5 minutes; season with salt and pepper. Transfer to a cutting board to cool, then cut into 1/2-inch chunks.
Using a food processor, puree the water, tahini, garlic, lemon juice and hot sauce. With the machine on, add the remaining 1/4 cup EVOO.
In a salad bowl, combine the eggplant, pita chips, chickpeas, giardiniera, cucumber, onion and parsley. Toss with the dressing.