Heat the olive oil in a large pot over medium heat. Add the chicken pieces and season with salt and pepper. Cook until the chicken is lightly browned on all sides.
Stir in the minced garlic and Italian seasoning. Cook for about 30 seconds until the garlic becomes fragrant.
Pour in the chicken broth and heavy cream. Add the penne pasta and bring the mixture to a gentle simmer.
Cover the pot and cook for 12 to 15 minutes, stirring occasionally, until the pasta is tender and most of the liquid has been absorbed.
Remove the pot from the heat. Stir in the Parmesan cheese, sun-dried tomatoes, and fresh spinach until the spinach wilts and everything is evenly combined.