Cook the pasta according to package instructions until al dente, then drain.
In a large skillet, heat olive oil over medium heat and add the chicken. Season with salt and pepper, cooking until browned and fully cooked, about 6-7 minutes per side.
Remove the chicken from the skillet and let it rest for a few minutes before slicing it into strips.
In the same skillet, add garlic and sun-dried tomatoes, cooking for about 1 minute until fragrant.
Add the spinach and cook until wilted, about 2-3 minutes, before pouring in the heavy cream and Parmesan cheese.
Stir in the cooked penne and the sliced chicken, mixing well to coat everything in the sauce.
Taste and adjust seasoning if needed, then let cook for an additional 2-3 minutes to heat through.
Serve immediately, garnished with additional Parmesan and fresh herbs if desired.