Make the dressing by whisking together olive oil, red wine vinegar, minced garlic, dried oregano, salt, and black pepper in a small bowl. Set aside.
Slice the hoagie rolls lengthwise without cutting all the way through, creating a hinge. Lightly toast them if desired.
In a large bowl, combine shredded lettuce, sliced red onion, halved cherry tomatoes, banana peppers, and chopped parsley.
Add the sliced salami, capicola or ham, and provolone cheese to the bowl with vegetables.
Pour the dressing over the salad mixture and toss gently until everything is evenly coated.
Divide the salad mixture evenly among the four prepared rolls, pressing gently to fit.
Serve immediately for the best texture and flavor.
