Cook the pasta according to the package instructions. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Add minced garlic and sauté for about 1 minute.
Add broccoli and cook for 3-4 minutes until tender-crisp.
Stir in shredded rotisserie chicken, heavy cream, and chicken broth. Bring to a simmer.
Add the cooked pasta and Parmesan cheese to the skillet. Toss everything together until well coated.
Season with salt and pepper to taste and serve immediately.