1.Preheat oven to 200°C/400°F. Oil four 3/4 cup ovenproof dishes with extra oil.
2.Heat 1 tablespoon olive oil in a medium frying pan over medium heat; cook red onion, mushrooms and parsley, stirring, until onion softens.
3.Remove pan from heat; stir in half of the brie cheese. Divide mushroom mixture among dishes; break 2 eggs into each dish.
4.Bake eggs 5 minutes; increase oven to 220°C/425°F. Sprinkle eggs with the remaining brie cheese; bake 5 minutes or until eggs set and cheese melts.