Preheat the oven to 180°C and set the grill to its highest setting.
Gently fry onions in oil over very low heat for 45 minutes until caramelised and golden-brown.
Place mushrooms in a baking dish, season with salt and pepper, and top with butter, garlic, and oil.
Bake the mushrooms in the oven for 10-12 minutes until slightly softened.
Combine cheese, mustard, garlic, and egg in a bowl and mix well.
Remove mushrooms from the oven and top each with caramelised onions and the rarebit mixture.
Grill the topped mushrooms until the cheese melts, bubbles, and turns golden-brown.
Serve one large coated mushroom on each plate.