Bring water to boil in a medium saucepan. Place frozen brussels sprouts in the water, and return to boil. Reduce heat, and simmer 6 to 7 minutes, until tender; drain.
In a medium bowl, mix brussels sprouts with butter, cream of mushroom soup, eggs, Cheddar cheese, and 1/3 cup bread crumbs. Transfer to a medium baking dish, and top with remaining bread crumbs.
Cover, and bake 25 minutes in the preheated oven, until bubbly. Uncover, and continue baking 5 minutes, until lightly browned.
