Place thinly sliced red onion in a small bowl of cold water and set aside for 10 minutes to reduce sharpness. Meanwhile, combine mayonnaise, red wine vinegar, garlic powder, oregano, salt, and black pepper in a large mixing bowl. Whisk together for 30 seconds until smooth and fully emulsified. Drain the onions, pat dry with paper towels, then add them to the bowl along with shredded lettuce and banana peppers. Toss everything together until every strand is coated and the salad looks glossy.

Slice each sub roll lengthwise, cutting about three-quarters of the way through to create a hinge. Divide the salami, pepperoni, and turkey evenly among the three rolls, layering the meats. Top each with 2-3 slices of provolone cheese, overlapping them slightly for complete coverage.

Position oven rack about 6 inches below the broiler element (usually second-highest position) and preheat broiler to high for 3-4 minutes. Place assembled sandwiches on a baking sheet and broil for 2 to 3 minutes, watching closely, until cheese is bubbling with golden-brown spots and meat edges begin to crisp.

Using oven mitts, carefully remove baking sheet from oven. Immediately layer tomato slices over melted cheese on each sandwich, then season tomatoes lightly with salt and black pepper.

Spoon generous amount of grinder salad onto each sandwich, distributing evenly from end to end. Finish by sprinkling grated parmesan cheese liberally over the salad. Gently close each sandwich, pressing down just enough to compact layers without squishing. Slice in half diagonally with a serrated knife.