This is really a great version of a salad you'd get at an Italian red sauce joint. It's crunchy and acidic, which is everything I want to eat with rich and fatty entrées.
Technique tip: Soaking onions in ice water ahead of time will kill some of their bite; marinating in vinegar, honey, salt and pepper along with the chiles helps soften them. You can cut the iceberg lettuce a few hours ahead and store it in a zippered bag in the refrigerator.
Swap option: Use romaine or escarole instead of iceberg, use red onion instead of white or yellow, use another firm cheese like Parmesan instead of pecorino.
Combine the chile, onion, vinegar and honey in a large bowl; season with salt and pepper and set aside for 5 or so minutes to soften and marinate the onion.2.
Add the olives and oregano to the onion and toss to coat.3.
Arrange the lettuce and parsley on a large serving platter or in a bowl. Spoon the onion-olive mixture over. Season with salt and pepper and drizzle with olive oil. Scatter with the cheese and more oregano, if desired, before serving.