To prepare the salad: Separate the layers of the onion, stack two or three layers on top of one another, and slice them lengthwise 1/16-inch thick. Repeat with the remaining onion layers. Place the onion slices in a small bowl of ice water and set them aside while you prepare the rest of the ingredients for the salad. Drain the onion and pat dry with paper towels before adding them to the salad.

Cut the iceberg in half through the core. Remove and discard the outer leaves from the head and remove and discard the core. Separate the lettuce leaves, stack two or three leaves on top of one another, and slice them lengthwise 1/4-inch thick. Repeat with the remaining leaves and thinly slice the radicchio in the same way.

Cut the tomatoes in half, season them with salt, and toss gently to distribute the salt.

Combine the lettuce, radicchio, tomatoes, ceci, provolone, salami, peperoncini, and onion slices in a large, wide bowl. Season with salt and toss to thoroughly combine the ingredients. Drizzle 1/2 cup of the vinaigrette and squeeze the lemon juice over the salad, then toss gently to coat the salad with the dressing. Taste for seasoning and add more salt, lemon juice or vinaigrette if desired. Pile the salad on a large platter or divide it among individual plates, piling it like a mountain. Sprinkle the dried oregano on top and serve.

To make the oregano vinaigrette: Combine the vinegar, oregano, lemon juice, smashed garlic, grated garlic, salt and pepper in a medium bowl and whisk to combine the ingredients. Set the vinaigrette aside to rest for 5 minutes to marinate the oregano. Add the olive oil in a slow, thin stream, whisking constantly to combine. Taste for seasoning and add more salt, pepper, or lemon juice, if desired. Use the vinaigrette or transfer it to an airtight container and refrigerate it for up to three days. Bring the vinaigrette to room temperature, whisk to recombine the ingredients, and taste again for seasoning before using. Makes a little more than a cup.