Pour in heavy cream and chicken broth, stirring to combine. Add Italian seasoning and red pepper flakes. Simmer until slightly thickened, adjusting consistency with reserved pasta water if needed.
Return chicken and pasta to the skillet with the sauce. Toss to coat, and cook for 2 minutes to meld flavors. Adjust seasoning if needed.
Sprinkle with Parmesan cheese and let it melt. Garnish with fresh parsley before serving.
Notes
For a richer flavor, use freshly grated Parmesan cheese.