Boil a large pot of salted water. Cook penne pasta according to package directions until al dente. During the last 3 minutes of cooking, add broccoli florets directly to the pasta water.
Reserve 1 cup of starchy pasta water in a measuring cup before draining.
Create the creamy sauce by pouring in heavy cream and chicken broth, then simmer gently for 2 to 3 minutes.
Add Parmesan and mozzarella cheese off the heat, whisking until smooth. Season with Italian seasoning, garlic powder, salt, pepper, and red pepper flakes.
Combine the drained pasta and broccoli with the creamy sauce, tossing gently to coat.
Fold in the shredded rotisserie chicken until warmed through.
Adjust the sauce’s consistency by adding reserved pasta water as needed.
Finish with a cold knob of butter just before serving.
Notes
Feel free to use leftover roasted chicken or experiment with different cheeses and pasta shapes.