Preheat the oven or toaster oven to 400 degrees Fahrenheit (204 degrees Celsius).
Slice the Italian hoagie roll lengthwise, keeping the hinge intact if possible.
Layer the Genoa salami, pepperoni, and ham evenly across the bottom half of the roll.
Place the provolone and sliced fresh mozzarella over the meat layer.
Place the sandwich open-faced on a baking sheet and toast for 4 to 5 minutes, or until the bread edges are golden and the cheese is bubbly and melted.
Remove the sandwich from the oven and add shredded lettuce, tomato slices, red onion, and banana peppers.
Drizzle the olive oil and red wine vinegar directly over the vegetables.
Season the sandwich with dried oregano, salt, and black pepper.
Close the sandwich halves, press down slightly, and slice diagonally to serve.