Preheat oven to 425 degrees F.
Prepare the vinaigrette. Blend together the preserved lemon with parsley, lemon, honey, tahini, and mustard. Slowly add the oil while the blender is on, blending until smooth. Season the dressing with salt and pepper. Set aside.
Dry the rinsed and drained chickpeas with clean towels. Toss the chickpeas with olive oil and salt and spread evenly on a baking sheet. Roast for 20-25 minutes or until golden brown and crispy. Sprinkle sumac on the chickpeas, tossing to coat.
Toss the radish wedges with olive oil, dried parsley, salt, and pepper and spread evenly on a baking sheet. Roast for 20-25 minutes or until charred and softened.
Toss the cut pita bread with olive oil and sesame oil. Spread on a baking sheet and sprinkle sesame seeds and salt on top. Toast for 5-7 minutes or until golden brown and crispy.
Prepare the remaining salad ingredients. Portion the lettuce into two bowls and top with the sliced egg, halved cherry tomatoes, chopped cucumber, crumbled feta, chopped parsley, scallions, mint, crispy sumac chickpeas, roasted radish, and sesame pita chips. Serve with the preserved lemon vinaigrette.