Preheat the oven to 350º and butter a 2 quart casserole dish.
Steam the broccoli for 15 minutes.
Mix soup, mayonnaise and egg in a large mixing bowl.
Add half of the cheese and all of the broccoli.
Pour the mixture in the casserole dish.
Add the remaining cheese on top.
Crush crackers and butter in a separate small mixing bowl and layer on top of cheese.
Bake at 350º for 35 minutes.