How to Make It
Preheat the oven to 475°F. In a large pot, fitted with a steamer basket, bring 1-inch of water to a boil. Place the broccoli in the steamer basket and cook, covered, until tender, about 7 minutes. Reserve 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 and 1/2 teaspoon each salt and pepper. Toss the sauce with the broccoli and place in an 8-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 15 minutes. Let cool slightly, serve.