Preheat oven to 165°C. Scoop out soft centre from bread roll bases to form a shell. Brush inside of bases and tops with a little butter. Place bases on a baking tray. Fill with spinach, then crack an egg into each, place a slice of cheese on. Season. Top with bacon.
Combine mushroom with thyme and remaining butter in an ovenproof dish. Bake rolls and mushrooms for 15 minutes. Add roll tops to the tray and bake for a further 5 minutes or until rolls are golden, bacon is crisp and eggs are set. Sandwich with tops and serve with mushroom.