In a small bowl whisk, together the olive oil, lemon juice, vinegar, shallot, garlic, oregano, salt and pepper and set aside.
Cut the iceberg lettuce into halves and remove the core. Slice the rest of it lengthwise into ¼ inch / ½ cm strips, then repeat with the radicchio.
In a large bowl combine the lettuce, radicchio, tomatoes, chickpeas, mozzarella, yellow cheese and if desired the salami. Drizzle with the dressing and toss gently to coat. Season with salt and pepper and toast again, then serve.