Thaw the broccoli, grease a small casserole dish, shred the cheese, and put about two cups of cheese nips in a plastic bag and crush with a cup or your hand.
Place broccoli, egg, soup, mayo, 3/4 of the cheese, and 3/4 of the crackers in a bowl. Stir and pour in casserole dish. Sprinkle the remaining crackers and cheese on top.
Place in 375 oven for about 30 minutes. Test with a toothpick. You can also do it on 350 for 45 minutes.