In a small bowl, whisk together the olive oil, lemon juice, red wine vinegar, shallot, garlic, and dried oregano. Season with salt and pepper to taste. Set aside.

Halve the iceberg lettuce and radicchio, remove cores, and slice into thin strips. Slice the red onion into rings and halve or quarter the cherry tomatoes.

In a large mixing bowl, combine all the prepared vegetables, chickpeas, mozzarella, provolone, and pepperoncini. Gently combine.

Drizzle the dressing over the salad, and use tongs to toss gently. Taste and adjust seasoning if necessary.

Transfer to a serving dish or keep in the mixing bowl. Garnish with fresh oregano and serve immediately.