In a skillet, add onion and butter and heat 3-5 minutes or until onion is tender. Add soup and mustard and mix well. Heat until the mixture just begins to bubble.
In a casserole dish, arrange half of the broccoli in the bottom. Add half of the soup mixture, half of the eggs and half of the cheese. Repeat layer.
Bake for 20 minutes. Sprinkle on onions and bake for an additional 5 minutes.