Make the pita chips: Preheat oven to 400°F. Toss pitas with olive oil, pepper, and salt in a medium bowl. Spread in an even layer on a large rimmed baking sheet lined using parchment paper. Bake until crispy and lightly browned, 8 to 10 minutes. Remove from oven, and let stand on baking sheet until completely cooled, about 10 minutes. (Alternatively, preheat an air fryer to 400°F for 10 minutes. Add pita mixture to basket, and cook until crisp and lightly browned, 5 to 8 minutes.)
Meanwhile, make the dressing: Place lemon juice, pomegranate molasses, sumac, honey, salt, and garlic in a blender; process until smooth, 30 seconds. With blender running, slowly add olive oil, processing until emulsified, about 30 seconds. Season with additional salt to taste.
Make the salad: Stir together lettuce, tomato, cucumbers, peppers, radishes, scallions, shallot, mint, and parsley in a large bowl. Toss with ⅔ cup dressing and salt until combined. Season with additional salt to taste. Top with crushed pita chips. Serve immediately with remaining ⅓ cup dressing.
