Cook the penne pasta according to package directions until al dente.
During the last 3 minutes of cooking time, add the broccoli florets directly to the pasta water.
Before draining, reserve 1 cup of starchy pasta water in a measuring cup.
Drain the pasta and broccoli together and set aside.
Making the Sauce
Heat olive oil and butter in your largest skillet over medium-low heat.
Cook the diced onion for 4-5 minutes until softened, then add minced garlic for 30 seconds until fragrant.
Pour in heavy cream and chicken broth, bringing the mixture to a gentle simmer for 2-3 minutes.
Remove the skillet from heat completely before adding cheese to prevent graininess.
Whisk in Parmesan and mozzarella until completely smooth, then season with Italian seasoning, garlic powder, salt, pepper, and red pepper flakes.
Combining Ingredients
Add the drained pasta and broccoli to the creamy sauce, tossing gently with tongs to coat everything evenly.
Fold in shredded rotisserie chicken last.
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 a restaurant-quality finish.
Notes
Make sure to reserve some pasta water before draining. It helps create a creamy sauce. Don’t rush the addition of cheese; removing the skillet from heat first prevents grainy cheese. Adjust the red pepper flakes for your desired spice level.