Prepare the broccoli: Wash the broccoli and cut it into small florets. Bring a pot of water to a boil and cook the broccoli for about 2–3 minutes, until bright green and slightly tender. Drain well and set aside.
Cook the pasta: Bring a large pot of salted water to a boil. Cook the elbow macaroni according to the package directions until al dente. Drain well and set aside.
Make the roux: Melt the butter in a large saucepan over medium heat. Add the flour and whisk continuously for about 1 minute until smooth.
Add the milk: Slowly pour in the milk while whisking constantly to prevent lumps. Continue cooking and stirring until the sauce thickens slightly.
Season the sauce: Stir in the garlic powder, onion powder, salt, and black pepper.
Add the cheese: Reduce the heat to low. Gradually add the cheddar, mozzarella, and Parmesan cheese, stirring until completely melted and the sauce is smooth and creamy.
Combine everything: Add the cooked macaroni and broccoli to the cheese sauce. Stir gently until the pasta and broccoli are evenly coated.
Prepare the baking dish: Lightly grease a 9 × 13-inch baking dish. Transfer the macaroni and broccoli mixture into the dish and spread it evenly.
Add the topping: Combine the breadcrumbs with the melted butter. Sprinkle the breadcrumb mixture and additional cheddar cheese evenly over the top.
Bake: Preheat the oven to 375°F (190°C). Bake for 25–30 minutes, or until the cheese is bubbling and the top is golden brown.
Rest and serve: Remove from the oven and let the mac and cheese rest for 5 minutes before serving.