Heat broiler. Cook the pasta according to the package directions.
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 1/2 cups of the cheese and stir until melted. Stir in the nutmeg, 3/4 teaspoon salt, and 1⁄4 teaspoon pepper.
Add the pasta and broccoli and toss to combine. Transfer to a broilerproof 8-inch square or another 1 1/2-quart baking dish. Sprinkle with the remaining 1⁄2 cup of cheese. Broil until golden, 3 to 4 minutes.