Place broccoli in a steamer basket over simmering water. Cover and steam for approximately 5 minutes. Chop into bite-sized pieces.
Preheat oven to 350 degrees.
In a large bowl, combine broccoli, soup, mayonnaise, butter, eggs, onion, salt, and pepper. Mix well.
Add 1 cup of cheese and mix again.
Place mixture in a medium buttered casserole dish. Sprinkle remaining cheese and crackers on top.
Bake for 30 to 40 minutes and let stand for 15 minutes before serving.