In a large pot of salted water, cook the pasta to al dente according to the package instructions; drain.
Add the oil to a large, deep skillet over medium-high heat. Once hot, add the chicken, spreading it out in an even layer. Sprinkle on the salt and black pepper. Let the chicken cook until browned on the first side, about 2 minutes, and then flip it and cook it for 1 to 2 minutes more (it doesn’t have to be fully cooked now, it will continue cooking).
Turn the heat down to medium. Stir in the garlic and cook for 1 minute, stirring frequently.
Turn the heat down again to medium-low. Add the chicken broth, heavy whipping cream, and dried Italian herb seasoning. Bring to a simmer and let it cook for 3 minutes, stirring frequently.
Stir in the sun dried tomatoes and Parmesan. Stir in the cooked pasta. Let it simmer to thicken the sauce, about 2 minutes, stirring frequently. Turn off the heat and stir in the baby spinach until wilted.
Serve garnished with parsley and additional Parmesan if desired.