Cook the pasta according to package directions until al dente. Reserve 1 cup of pasta water before draining.
Heat olive oil in a large skillet over medium-high heat. Season chicken with salt and pepper; cook until browned and cooked through. Remove from skillet and set aside.
Add onion to the skillet; cook until softened, about 3-4 minutes. Add garlic; cook for 1 minute until fragrant.
Stir in sun-dried tomatoes; cook for 1-2 minutes.
Pour in chicken broth; bring to a simmer, scraping up any browned bits. Add heavy cream and Parmesan cheese; stir until cheese is melted and sauce is smooth.
Stir in spinach and cook until wilted, about 1-2 minutes.
Add cooked chicken to skillet with sauce.
Add cooked pasta to the skillet and toss to coat in the sauce. If the sauce is too thick, add a little of the reserved pasta water until it reaches your desired consistency.
Season with salt and pepper to taste.
Garnish with fresh parsley and additional Parmesan cheese, if desired. Serve immediately.