Preheat barbecue plate on medium-high heat. Brush the onions with oil and place on the barbecue to cook for 5-8 minutes or until tender, transfer to a plate.
Brush the mushrooms lightly with oil and place them o the barbecue, stem side-up for 4 minutes. Turn them over and cook for a further 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
Mix the grated beetroot and mayonnaise together. Spread over bun bases. Top each with salad leaves, tomato slices, and mushrooms. Season to taste and serve.
Tip: You can substitute Taleggio with any good melting cheese like Fontina, Edam or Gouda.