Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9x13 inch baking dish.

Cook broccoli in a large pot of salted boiling water until just slightly tender. Drain.

In a large bowl, combine eggs, onion, mushroom soup and mayonnaise.

Place a layer of broccoli in the prepared baking dish. Pour mayonnaise sauce over broccoli. Spread stuffing mix over the sauce. Drizzle butter or margarine over all and top with shredded cheese.

Bake at 350 degrees F (175 degrees C) for 30 minutes.