How to Make It
Preheat the oven to 475°F.
Cook the pasta in a large pot of boiling salted water until al dente. Add the broccoli to the pasta cooking water after the pasta has cooked 6 minutes. When the pasta is al dente and the broccoli is crisp tender drain the pasta and broccoli.
In a medium saucepan, melt 2 tablespoons of the butter over medium high heat until hot. Stir in the flour and cook, stirring, 2 minutes. Whisk in the milk in a steady stream and bring to a boil, whisking. Boil the milk sauce until slightly thickened, about 5 minutes. Stir in the cheddar, 1 teaspoon salt and 1/2 teaspoon pepper. Toss the sauce with the pasta and broccoli and place in a 13-by-9-inch square baking dish.
In a small heavy skillet, melt the remaining 1 tablespoon butter over low heat then toss the breadcrumbs in the butter. Sprinkle the breadcrumbs over the gratin.
Bake the gratin until the breadcrumbs are golden and the cheese sauce is bubbling around the edges of the dish, about 25 minutes. Let cool slightly, then serve.