Bring a large pot of salted water to a boil and cook the penne pasta until al dente, according to the package directions.

During the last 3 minutes of cooking, add the broccoli florets directly to the pasta water.

Before draining, reserve 1 cup of the starchy pasta water in a measuring cup. Drain the pasta and broccoli together and set aside.

In your largest skillet, heat olive oil and butter over medium-low heat. Cook the diced onion for 4–5 minutes until softened. Add the minced garlic and cook for another 30 seconds until fragrant.

Pour in the heavy cream and chicken broth, bringing the mixture to a gentle simmer for 2–3 minutes.

Remove the skillet from heat entirely before adding cheese to prevent graininess. Whisk in Parmesan and mozzarella until smooth, then season with Italian seasoning, garlic powder, salt, pepper, and optional red pepper flakes.

Add the drained pasta and broccoli to the creamy sauce, tossing gently with tongs to coat everything evenly.

Fold in the shredded rotisserie chicken last, then add reserved pasta water 2 tablespoons at a time until you reach a creamy, glossy consistency.

Stir in a cold knob of butter just before serving for that restaurant-quality finish.