Start by adding the chopped romaine and radicchio to a large mixing bowl.
Layer the mozzarella cubes, salami sticks, chickpeas, black olives, diced bell pepper, cucumber, pepperoncini slices, halved grape tomatoes, and red onion evenly over the greens.
Drizzle the prepared dressing over everything, then toss gently to coat all ingredients without bruising the salad.
Sprinkle the shaved Parmesan on top as a flavorful finishing touch.
To make the dressing, whisk together olive oil, red wine vinegar, Dijon mustard, grated garlic, oregano, and crushed red pepper flakes in a small bowl.
Season the dressing with kosher salt and freshly ground black pepper according to your taste, then stir well before pouring on the salad.