Preheat barbecue plate on medium-high heat. Spray prosciutto and onions with oil. Barbecue prosciutto for 1 minute each side until golden, transfer to a plate. Barbecue onions 5-8 minutes or until tender, transfer to a plate. Spray mushrooms lightly with oil. Barbecue mushrooms stem side-up 4 minutes, turn over and barbecue 3 minutes, or until tender.
Turn mushrooms over, top evenly with onions and cheese. Close barbecue hood (or cover mushrooms with an upturned roasting pan) cook 2-3 minutes until cheese is melted
Combine beetroot relish and mayonnaise. Spread over bun bases. Top each with salad leaves, tomato slices, prosciutto and mushrooms. Season to taste and serve.