Heat olive oil in a large pot or deep skillet over medium-high heat.
Add the chicken pieces and cook for 5-6 minutes, stirring occasionally, until browned and cooked through. Remove the chicken from the pot and set aside.
In the same pot, add the chopped onion and cook for 3-4 minutes until softened.
Add the minced garlic, dried Italian seasoning, salt, and black pepper. Cook for 1 minute, stirring frequently to release the aromas.
Add the uncooked 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 12-15 minutes, stirring occasionally, until the pasta is tender and most of the liquid is absorbed.
Return the cooked chicken to the pot and stir in the grated Parmesan cheese and chopped spinach.
Cook for an additional 2-3 minutes until the spinach wilts and the chicken is heated through.
Taste and adjust seasoning with additional salt and pepper if needed.
Serve hot, garnished with extra Parmesan if desired.