Prepare the vegetables: Remove any limp leaves from the lettuce, slice thinly, and soak the onion if necessary. Slice the tomato and drain the pepperoncini.

Make the grinder salad dressing: Combine mayonnaise, red wine vinegar, and olive oil in a bowl. Whisk in remaining dressing ingredients until smooth.

Build the grinder salad: Toss lettuce, onion, and pepperoncini in the dressing. Adjust seasoning and add Parmesan if desired. Set aside.

Prepare and toast the roll: Preheat oven broiler and toast the rolls cut-side up with butter or oil for 1-3 minutes.

Add cheese and melt: Layer provolone slices on the toasted rolls and return to broiler until melted.

Layer the meats: Arrange Genoa salami, ham, and optional pepperoni on the bottom roll.

Add tomatoes and season: Place tomato slices on the meats and season with salt and pepper.

Top with grinder salad: Pile the dressing-coated salad over the tomato layer.

Close and set the sandwich: Fold the top of the roll and let rest for 3-5 minutes.

Slice and serve: Cut the sandwich diagonally and serve warm.