Heat olive oil in a large pot over medium heat.
Add diced onion and cook for 3-4 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add ground chicken to the pot and cook, breaking it up with a spoon, until browned and cooked through, about 5-7 minutes.
Add penne pasta, diced tomatoes with their juice, chicken broth, water, dried oregano, dried basil, salt, and black pepper to the pot. Stir to combine.
Bring the mixture to a boil, then reduce heat to medium-low and cover the pot.
Simmer for 12-15 minutes, stirring occasionally, until the pasta is cooked and most of the liquid is absorbed.
Stir in chopped spinach and cook for 2 minutes until wilted.
Remove the pot from heat and stir in grated Parmesan cheese until melted and combined.
Serve hot.