Add the pasta to a large pot of boiling water. Set the timer for 7 minutes.
Meanwhile, rinse and chop the broccoli into bite sized florets. When the pasta has cooked for 7 minutes, add the broccoli to the pot and continue cooking for 3 minutes or until the pasta is al dente and the broccoli is bright green and tender crisp.
While the pasta is cooking, make the cheese sauce. Melt the butter in a small saucepan over medium heat. Whisk in the flour and continue whisking for 1 minute.
Whisk in the milk slowly. Cook over medium heat, whisking constantly, until the sauce thickens, about 5 minutes. Remove from the heat and stir in the grated cheese until smooth and creamy.
Drain the pasta and broccoli and return to the pan. Stir in the chopped chicken. Top with the cheese sauce, stir to coat, and sprinkle with salt and pepper.
This recipe does not produce a ton of cheese sauce. The pasta, chicken, and broccoli will be lightly coated in sauce. If you like your pasta dishes more saucy, double the amount of cheese sauce.