In a small mixing bowl, whisk together olive oil, red wine vinegar, lemon juice, Italian seasoning, granulated sugar, garlic powder, red pepper flakes, kosher salt, and black pepper until fully combined. Set aside.

Thinly slice the iceberg lettuce, tomatoes, red onion, pepperoncini peppers, and black olives. Arrange them on a cutting board or work surface.

Layer the assorted deli meats and provolone cheese on top of the chopped vegetables. Using a large knife, chop everything together until well combined.

Spread butter on the inside of the hoagie rolls and toast them in a skillet or oven until golden and crispy (about 2-3 minutes).

Drizzle 2 tablespoons of the Homemade Italian Dressing onto the bottom half of each toasted roll. Spread mayonnaise on the top half if desired.

Transfer the chopped meat, cheese, and vegetable mixture onto the dressed rolls. Close the sandwich and press gently.

Slice in half and serve immediately with extra dressing on the side.