Fill a large saucepan with salted water and bring it to a rolling boil.
Add the dried pasta and cook according to the package instructions until it reaches an al dente texture.
Place the broccoli florets into the boiling water during the final 4 minutes of the pasta’s cooking time.
When both the pasta and broccoli are tender, drain them thoroughly and set them aside. Do not rinse the pasta.
In a small bowl, blend the cornstarch with 2 tablespoons of cold water until a smooth slurry forms.
Using the same saucepan, combine the chicken broth, half-and-half, cornstarch slurry, onion powder, and garlic salt.
Whisk the ingredients together over medium heat. Bring the mixture to a simmer, continuing to whisk until it begins to boil and develops a thick, creamy consistency.
Remove the saucepan from the heat once the sauce has thickened.
Stir the sharp cheddar and Parmesan into the hot sauce until the cheeses are fully melted and the mixture is uniformly smooth.
Return the drained pasta and broccoli to the saucepan.
Gently toss everything together until the pasta and broccoli are evenly coated with the cheese sauce.
Season with the salt and ground black pepper, adjusting the quantities to taste.
Serve immediately to preserve the smooth texture of the sauce.