Preheat your oven to 350°F (175°C). Prepare a 13 x 9-inch baking dish by coating it with cooking spray.
In a large mixing bowl, thoroughly combine the cooked broccoli, mayonnaise, grated cheddar cheese, cream of mushroom soup, and lightly beaten eggs.
Transfer the broccoli mixture into the prepared baking dish, spreading it evenly.
Sprinkle the crushed crackers over the top of the broccoli mixture. Drizzle the melted butter evenly across the crackers.
Bake in the preheated oven for about 35 minutes, or until the casserole is set and the top is golden brown.
Allow the casserole to rest for a few minutes before serving.