Preheat air fryer to 375°. In a small bowl, combine green onions, parsley and 2 teaspoons mustard. In another bowl, mix bread crumbs, ketchup, seasonings and remaining 2 teaspoons mustard. Add beef to bread crumb mixture; mix lightly but thoroughly., Shape mixture into 8 thin patties. Place sliced cheese in center of 4 patties; spoon green onion mixture over cheese. Top with remaining patties, pressing edges together firmly, taking care to seal completely. , In batches, place burgers in a single layer on tray in air-fryer basket. Cook 8 minutes. Flip; cook until a thermometer inserted in burger reads 160°, 6-8 minutes longer. Serve burgers on buns, with toppings if desired.