Cheesy Baked Shells & Broccoli

5 cups medium pasta shells
1 tablespoon butter
2 tablespoons all-purpose flour
2 cups milk
2 cups coarsely grated Cheddar or Gruyere -- (8 ounces)
1/8 teaspoon ground nutmeg
kosher salt & black pepper
1 16 ounce bag broccoli florets -- thawed

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.