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In a large bowl, combine the shredded iceberg lettuce, thinly sliced red onion, and sliced banana peppers.
In a small bowl, whisk together the mayonnaise, red wine vinegar, olive oil, dried oregano, salt, and black pepper until smooth.
Pour the dressing over the lettuce mixture and toss gently to coat; set the grinder salad aside.
Split each hoagie roll lengthwise; on the bottom half of each roll, layer two slices of provolone cheese.
Evenly distribute the deli turkey breast, deli ham, Genoa salami, and pepperoni over the cheese; if using the optional tomato, add the tomato slices now.
(Optional) Place the assembled bottom halves under a broiler for 1–2 minutes, until the cheese is melty and the meats are slightly warmed.
Generously pile the prepared grinder salad on top of the meats and cheese, then place the top half of the roll over the salad.
Slice each grinder sandwich in half and serve immediately; if you have leftovers, store the salad and the assembled meat/cheese rolls separately in the refrigerator and combine just before eating.