Preheat your oven to 400°F. As it heats, arrange the broccoli florets and diced cooked chicken evenly in a 9-inch pie dish or shallow baking dish.
In a small mixing bowl, combine the condensed soup with milk and stir until smooth. Pour this mixture evenly over the broccoli and chicken, allowing it to settle into the gaps. Sprinkle the shredded cheddar cheese over the top.
In another small bowl, stir together the bread crumbs and melted butter until well combined. Scatter the buttered crumbs evenly over the cheese layer.
Place the dish in the preheated oven and bake for 20 minutes, or until the cheese is melted and bubbling and the casserole is heated through. Serve warm.