Bring a large pot of salted water to a boil and cook the rotini pasta until al dente. During the last 3 minutes, add the broccoli florets. Drain together and reserve 1 cup of pasta water.
In the same pot, heat the olive oil over medium heat. Add the garlic and sauté until fragrant.
Pour in the heavy cream and milk. If using cream cheese, whisk it in until smooth and melted.
Stir in Parmesan cheese, Italian seasoning, salt, black pepper, and red pepper flakes (optional). Let the sauce thicken slightly. Add reserved pasta water as needed.
Add the cooked pasta, broccoli, and shredded rotisserie chicken. Toss until evenly coated and creamy.
Serve warm with extra Parmesan on top.