Bring a large pot of salted water to a rolling boil over high heat. Carefully drop the fresh broccoli florets into the water. Boil for exactly 2 minutes to tenderize them slightly while locking in that vibrant green color. Immediately drain and plunge the florets into a bowl of ice water.

In your large mixing bowl, combine the cream of mushroom soup, mayonnaise, shredded sharp cheddar cheese, and beaten eggs. Add the finely chopped yellow onion, salt, and black pepper. Stir vigorously until the mixture is completely smooth.

Gently fold the cooled, thoroughly drained broccoli florets into the creamy cheese sauce. Pour the mixture into a greased white oval ceramic baking dish. Use a spatula to spread it into an even, flat layer.

In a small bowl, mix the plain breadcrumbs with the melted butter. Sprinkle this buttered mixture generously and evenly over the top of the casserole in the baking dish.

Bake uncovered in a preheated oven at 350°F (175°C) for 35 to 40 minutes. The casserole is done when you hear the creamy, cheesy sauce actively bubbling around the edges and the top is deep golden brown.

Remove the dish from the oven and let it rest for 5 to 10 minutes. Garnish the top with freshly chopped parsley and serve warm.