Bring a large pot of salted water to a rolling boil. Add the penne pasta and cook for 8–10 minutes until al dente. Add the broccoli florets 3 minutes before the pasta is done. Reserve 1 cup of pasta water before draining.

In a large skillet over medium heat, combine 2 tablespoons of olive oil and 2 tablespoons of butter. Sauté the diced onion for 3–4 minutes until soft, then add minced garlic and cook for another 30 seconds.

Pour in 1 cup of heavy cream and ½ cup of low-sodium chicken broth into the skillet with the sautéed vegetables. Let it simmer for 2–3 minutes over low heat.

Remove the skillet from heat and whisk in 1 cup of Parmesan and ½ cup of mozzarella until fully melted. Add the Italian seasoning, garlic powder, and red pepper flakes.

Toss the drained pasta and broccoli into the cheese sauce. Gently fold in the shredded rotisserie chicken until heated through.

Gradually add the reserved pasta water while stirring to achieve the desired creaminess. Finish with a small knob of cold butter.