In a large skillet or saucepan, heat olive oil and butter over medium-high heat until the butter is melted.
Add the cubed chicken and minced garlic to the pan. Cook for 5–7 minutes, stirring occasionally, until the chicken is golden and cooked through, and the garlic is fragrant.
Pour in the chicken broth and bring to a gentle boil. Add the penne pasta and Italian seasoning, stirring well. Let it cook for about 10 minutes, stirring occasionally, until the pasta is al dente and most of the broth has been absorbed.
Lower the heat to medium-low. Stir in the heavy cream, spinach, and sun-dried tomatoes, and cook for 2–3 minutes until the spinach is wilted and the sauce begins to thicken.
Add the Parmesan cheese, stirring until everything is well combined and the cheese is melted.
Cut the chicken evenly: Keeping the chicken pieces similar in size helps them cook quickly and evenly without drying out.
Stir the pasta occasionally: Stirring as the pasta cooks in the broth prevents sticking and helps release starch, which thickens the sauce.
Adjust the sauce as needed: If the sauce seems too thick, add a splash of chicken broth. If it’s too thin, let it simmer uncovered for a minute or two.
Add the cheese off high heat: Lower the heat before stirring in the Parmesan so it melts smoothly into the sauce without clumping.