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 chicken from the pot and set aside.
In the same pot, add the diced onion and cook for 3-4 minutes until softened.
Add the minced garlic, dried Italian seasoning, salt, and black pepper. Cook for 1 minute until fragrant.
Pour in the diced tomatoes with their juice and chicken broth. Stir to combine.
Add the uncooked penne pasta to the pot and stir to submerge the pasta in the liquid.
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 fresh baby spinach leaves. Cook for 2 minutes until the spinach wilts.
Remove the pot from heat and stir in the grated Parmesan cheese until melted and well combined.
Serve hot.