Add all dressing ingredients to a large jar. Season with about 1/4 teaspoon each of salt & pepper. Seal and shake until smooth and fully combined. Chill for best flavor and shake again before using.
Spread shredded lettuce evenly across a large cutting board. Sprinkle diced onion, banana peppers, and pickles over the top.
Evenly layer pepperoni, salami, ham, and provolone over the veggies.
Use a large knife to chop everything together, first in one direction, then crosswise. Keep chopping until finely diced to your liking.
Drizzle dressing over the mixture to taste. Chop again to evenly coat everything. Add more dressing if needed.
Slice hoagie rolls in half and toast until lightly golden. Spread both sides with mayo. Add tomato and avocado if using.
Spoon the chopped mixture into the rolls, packing it in well. Serve right away.
Video
Notes
Note 1: This makes more dressing than you’ll need, but I like having extra. Store in the fridge for up to 1 week and shake well to recombine. Use on more sandwiches, veggies, or salads. It’s so good!Storage: Sandwiches are best eaten right after assembling. The filling doesn’t store well once dressed.