Sauté onion in butter in a medium skillet over medium heat until tender.
Combine eggs, salt, pepper, cheese, mushrooms, and peas, if desired, in a small mixing bowl; stir gently, and add to onion in skillet. Cook, stirring frequently, until eggs are set but still moist and cheese begins to melt. Transfer egg mixture to a warm serving plate; sprinkle with parsley. Serve immediately.