Heat oven to 200C/fan 180C/gas 6. Tip the potatoes and shallots into a large, non-stick roasting tin, drizzle with the oil, sprinkle over the oregano, then mix everything together well. Bake for 15 mins, add the mushrooms, then cook for a further 10 mins until the potatoes are browned and tender.
Make four gaps in the vegetables and crack an egg into each space. Return to the oven for 3-4 mins or until the eggs are cooked to your liking.