Add the chickpeas to a food processor and pulse 5 to 10 times, or until they take on a flaky texture. Transfer to a large serving bowl.
Next, add the artichoke hearts to the food processor. Pulse about 10 times, or until they're chopped and take on a flaky texture. Transfer to the serving bowl.
Stir in the cucumbers, tomatoes, onion, olives, pepperoncini, parsley, mayonnaise, lemon juice, and shawarma spice mix. Stir well to combine.
Taste and season with salt, if desired.
Serve alongside crackers, warm pita bread, or on its own.
Refrigerate leftovers in an airtight container for up to 5 days.