Bring a large pot of salted water to a boil. Add the penne pasta and cook for 10-12 minutes. For the last 3 minutes, add the broccoli florets. Reserve 1 cup of pasta water, then drain.

In a skillet, heat olive oil and butter over medium-low heat. Add diced onion, sauté for about 5 minutes until translucent. Stir in minced garlic and cook for 30 seconds.

Add heavy cream and chicken broth to the skillet. Increase heat to a gentle simmer, stirring occasionally.

Remove from heat and whisk in Parmesan and mozzarella until smooth. Season with Italian seasoning, garlic powder, salt, pepper, and red pepper flakes.

Add drained pasta and broccoli to the sauce, mixing gently. Fold in shredded rotisserie chicken.

Add reserved pasta water gradually to achieve desired creaminess.

Stir in a knob of cold butter before serving.