Slice the hoagie rolls in half and toast them until lightly golden and crisp on the inside while still soft on the outside. Set them aside while you prepare the filling.
On a large cutting board, pile the shredded lettuce, ham, soppressata, Genoa salami, pepperoni, provolone cheese, red onion, and beefsteak tomato together. Using a large chef's knife or cleaver, chop everything together until the ingredients are evenly mixed into small, bite-sized pieces.
Add the mayonnaise, hot hoagie spread, red wine vinegar, olive oil, minced garlic, pepperoncini peppers, black pepper, oregano, crushed red pepper flakes, and salt directly onto the chopped mixture. Continue chopping and folding everything together until the dressing evenly coats every bite.
Divide the chopped Italian mixture evenly among the toasted hoagie rolls, gently pressing the filling into each roll so every sandwich is packed full. Top each sandwich with a generous handful of lightly crushed potato chips for extra crunch.
Wrap each sandwich tightly in sandwich paper or parchment paper and let them rest for 5 minutes. This helps the flavors meld together while allowing the bread to absorb just enough of the dressing without becoming soggy.
Slice each sandwich in half and serve immediately. These sandwiches are perfect for lunches, tailgates, picnics, or whenever you're craving a deli-style sub loaded with bold Italian flavors.