Cut the broccoli into small florets (peel and chop the stems and save for another use, like the kids' lunch. Blanch the broccoli in boiling water for 1 minute, then immediately drain and shock in a bowl of ice water to stop the cooking. This will keep the broccoli green.
Preheat the oven to 375°F Butter an 8 x 10-inch baking dish.
Gently warm the mushroom soup in a sauce pan over low heat.
Using a wooden spoon or spatula, combine the broccoli, Cheddar cheese, sliced onion, rice, scallions, salt and pepper, soup and half of the Parmesan in a large mixing bowl.
In a small bowl, combine the melted butter and bread crumbs. Transfer the broccoli-rice mix to the baking dish and spread evenly. Sprinkle the remaining Parmesan over the top and then sprinkle the bread crumbs over the cheese. Bake the casserole, uncovered, for 20 minutes. Raise the heat to 425°F and cook 5 more minutes, to brown the top if it has not browned already. The sides of the casserole should be bubbling gently.
Let the casserole stand for 10 to 15 minutes before serving.