Heat olive oil in a large pot or deep skillet over medium heat.
Add the chicken pieces and cook for 5-6 minutes until browned and cooked through. Remove chicken from the pot and set aside.
In the same pot, add the chopped onion and minced garlic. Sauté for 2-3 minutes until fragrant and translucent.
Add the penne pasta, chicken broth, and diced tomatoes (with their juice) to the pot. Stir to combine.
Bring the mixture to a boil, then reduce heat to medium-low. Cover and simmer for 10-12 minutes, stirring occasionally, until the pasta is al dente and most of the liquid is absorbed.
Return the cooked chicken to the pot. Stir in the chopped spinach, heavy cream, dried oregano, and dried basil.
Cook for an additional 3-4 minutes until the spinach wilts and the sauce is creamy.
Season with salt and black pepper to taste.
Remove from heat and stir in the grated Parmesan cheese until melted and well combined.
Serve hot, garnished with extra Parmesan if desired.