Pre-heat your oven to 350°F (175°C) and lightly grease your baking dish.
Prepare the broccoli: Cut the broccoli into bite-sized pieces and steam until just tender, about 5 minutes. Spread the steamed broccoli in the baking dish.
Make the cheese sauce: In your saucepan, melt the butter over medium heat. Stir in the flour until smooth. Gradually whisk in the milk, then cook and stir until the sauce thickens and comes to a boil. Remove from heat and stir in the cheese until melted. Season with salt and pepper.
Assemble the casserole: Pour the cheese sauce over the broccoli in the baking dish, stirring to ensure all the broccoli is coated. Sprinkle the bread crumbs evenly over the top.
Bake the casserole: Bake in the preheated oven for 20-25 minutes, or until the top is bubbly and golden.