Cook the pasta in a large pot of salted water according to package directions.
Add the chopped broccoli to the pot during the last 4 minutes of cooking time.
While the pasta cooks, prepare the sauce.
In a small saucepan, combine the semisoft garlic and herb cheese and the milk.
Cook over medium heat, stirring constantly, until the cheese is fully melted and the sauce is smooth and creamy.
Before draining, reserve about 1/4 cup (960 ml) of the starchy pasta water.
Drain the pasta and broccoli, and return the mixture to the hot pot.
Pour the creamy cheese sauce over the pasta and broccoli.
Toss gently to coat everything evenly. If the sauce is too thick, add a splash of the reserved pasta water to reach your desired consistency.
Serve immediately, sprinkled generously with finely shredded Asiago or Parmesan cheese.
Finish the dish with a sprinkle of fresh parsley or chives for a burst of fresh flavor and color.