Cook pasta according to package directions until al dente. Drain and set aside.
Heat olive oil in a large skillet over medium heat. Add garlic and sauté for about 1 minute until fragrant.
Pour in heavy cream and chicken broth. Stir and gently simmer for 5 minutes until slightly thickened.
Stir in shredded chicken and spinach. Cook for 2 minutes until spinach is wilted.
Add cooked pasta and toss to coat. Stir in Parmesan cheese and season with salt and pepper to taste.
Serve warm with extra Parmesan if desired.