While the sliders are baking, prepare the grinder topping. In a large bowl, combine the mayonnaise, red wine vinegar, Italian seasoning, banana pepper juice, and Parmesan cheese. Whisk until smooth. Taste and adjust the seasoning, if desired.
Add the shredded iceberg lettuce, chopped banana peppers, and sliced red onion to the dressing. Toss until the vegetables are evenly coated.
Remove the sliders from the oven and carefully lift off the top buns. Spoon the grinder topping evenly over the meat and melted cheese. Replace the top buns, slice into individual sliders, and serve immediately. Enjoy!