Preheat an oven to 260 degrees C. Split the rolls open and toast them on a baking tray in the oven while it is preheating. Mix together the mayonnaise, garlic and Parmesan cheese in a small bowl. Refrigerate until ready to use. Remove the rolls from the oven when toasted as desired.
Heat olive oil in a large frying pan over medium-high heat. Carefully place the schnitzel and onions in the frying pan and season with sea salt, Worcestershire sauce and liquid smoke. Cook and stir until the steak is browned and the onion is tender, about 10 minutes.
Generously spread the prepared garlic-Parmesan mayonnaise on both halves of the toasted rolls. Divide the steak and onion mixture evenly among the bottom halves of the rolls, piling them high. Top each with 2 slices of cheese then sprinkle with Italian seasoning. Place the tops on the sandwiches.
Bake the sandwiches on a baking tray in the preheated oven until the cheese is melted, about 5 minutes.