Combine all the ingredients for the dressing in a small bowl. Set aside.
½ cup mayo, 3 tablespoon olive oil, 2 tablespoon red wine vinegar, ⅛ teaspoon paprika, ⅛ teaspoon poppy seeds, ⅛ teaspoon celery salt, ⅛ teaspoon red pepper, ½ teaspoon Italian seasoning, salt and black pepper to taste
Finely chop the lettuce, slices of ham, salami, pepperoni, slices of provolone cheese and pepper jack cheese, tomatoes, red onion, banana peppers and Parmesan. Add all ingredients for the grinder salad to a large mixing bowl.
2 cups shredded iceberg lettuce, 6 slices ham, 6 slices pepperoni, 6 slices hard salami, 3 slices provolone cheese, 3 slices pepper jack cheese, 1 cup diced cherry tomatoes, ½ small red onion, ¼ cup banana peppers, ¼ cup shredded Parmesan cheese
Pour the dressing over the top of the grinder salad ingredients, a little at a time, and, using tongs, mix everything to combine. Store any excess dressing in the refrigerator for later use.
Stuff the grinder salad into the sub rolls and serve.
4 Italian sub rolls