Boil water, add broccoli, cook 2 minutes, drain.
Preheat oven to 400°F.
In a bowl, combine condensed cream of mushroom soup, mayonnaise, milk, eggs, chopped onion, and shredded cheddar cheese. Mix well and season with salt and pepper.
Add the drained broccoli to the mixture and stir to coat.
Grease a 9x13-inch baking dish. Transfer the broccoli mixture to the baking dish.
In a small bowl, combine the crushed crackers and melted butter.
Scatter the cracker crumbs over the casserole.
Place in the preheated oven and bake for 35 to 45 minutes, or until the casserole bubbles and the topping is golden brown.
Let rest for a few minutes before serving.