Preheat oven to 350 degrees. Butter a 9×13 baking dish.
In a medium bowl, whisk together mushroom soup, mayonnaise, eggs, and onion.
Place broccoli in a very large mixing bowl. Stir in the soup mixture and thoroughly combine. Stir in the shredded cheese.
Spread mixture into your casserole dish, and sprinkle with salt, pepper, and paprika. Bake 45-60 minutes in a preheated oven, until the top has started to brown.