Cut ham, salami and provolone into small pieces on a large clean board. Add romaine, celery, roasted peppers and pepperoncini and chop together until pieces are about 1/4 inch, keeping some texture.
Stir mayonnaise, vinegar, oil, oregano and pepper in a large bowl. Add the chopped mixture and fold until lightly dressed.
Split the rolls lengthwise without cutting through the hinge. Remove only a little loose crumb if needed to make room for the filling.
Divide the chopped mixture equally among the rolls, spreading it along their full length. Close gently and rest for 2 minutes so the filling settles.
Cut each sub across the middle and serve promptly. Keep any waiting portions refrigerated and use the same day for the best crunch.