Begin by bringing a large pot of salted water to a rolling boil. Add the penne pasta to the pot and cook according to the package instructions until al dente, usually around 10-12 minutes. Just three minutes before the pasta finishes cooking, toss in the broccoli florets to blanch them. When done, drain the pasta and broccoli together, setting aside a cup of pasta water for later.

In a large skillet, heat 2 tablespoons of olive oil and 1 tablespoon of butter over medium-low heat. Once the butter melts, add diced yellow onion and sauté for about 4-5 minutes until they turn translucent. Then, stir in 2 cloves of minced garlic and cook for an additional 30 seconds.

Pour in 1 cup of heavy cream and 1 cup of chicken broth into the skillet with the onions and garlic. Stir the mixture well, allowing it to come to a gentle simmer for about 2-3 minutes.

Remove the skillet from heat, then whisk in ½ cup of grated Parmesan cheese and 1 cup of shredded mozzarella until the cheese is fully melted and the sauce is smooth. Season with 1 teaspoon of Italian seasoning, a pinch of garlic powder, and salt and pepper to taste.

Add the drained pasta and blanched broccoli to the creamy cheese sauce, followed by 2 cups of shredded rotisserie chicken. Gently toss everything until well combined.

Gradually pour in the reserved pasta water, a little at a time, until the sauce reaches your desired consistency.

For an extra silky finish, stir in a small knob of cold butter just before serving.