Preheat an oven to 325 degrees F (165 degrees C).
Beat the eggs in a mixing bowl; whisk in the mayonnaise, cream of mushroom soup, broccoli, Cheddar cheese, onion, and butter. Spoon into a 2 quart casserole dish; sprinkle with the crushed crackers.
Bake in the preheated oven until hot and bubbly, 30 to 40 minutes.
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