Heat broiler. Cook the pasta according to the package directions. Drain.
Meanwhile, heat the butter in a large pot over medium heat. Add the flour and cook, stirring, for 2 minutes.
Whisk in the milk and cook, stirring occasionally, until slightly thickened, 4 to 5 minutes.
Add 1 ½ cups of the cheese and stir until melted. Stir in the nutmeg, ¾ teaspoon salt, and ¼ teaspoon pepper.
Add the pasta and broccoli and toss to combine. Transfer to a broilerproof 8-inch square or a 1 ½-quart baking dish.
Sprinkle with the remaining ½ cup of cheese. Broil until golden, 3 to 4 minutes.