In a mortar and pestle or mini chopper, combine the anchovies and garlic with a big pinch of salt and many grinds of black pepper. Pulverize until a paste forms.

Scrape into a medium bowl and whisk in lemon juice, olive oil, and Aleppo pepper until combined. Taste and season with more salt and black pepper, if needed.

Use the flat side of a chef’s knife to smash the olives and loosen the pits, then tear the flesh into 2 or 3 pieces (discard pits). Cut peppers in half lengthwise, then halve crosswise. Place the olives and peppers in a salad bowl.

Trim the celery at both ends, then separate the bunch into individual stalks; wash and dry. Snap off the light green leaves from innermost stalks and set those aside. Cut the celery into very thin slices on a dramatic angle, then transfer to the bowl with the olives and peppers.

Use a vegetable peeler to shave half the Parmigiano over. Add most of the dressing and toss with your hands to coat. Add the parsley and reserved celery leaves and toss gently to combine.

Shave the other half of the Parm over, drizzle with dressing, and top with a few more grinds of black pepper.