Heat oil in a large pot and cook onion and carrots for 5 minutes. Add garlic and oregano and stir for 30 seconds.
Add tomatoes, broth, chicken, beans, salt and pepper. Bring to a gentle simmer.
Cook for 20 to 25 minutes until the chicken reaches 165°F and the carrots are tender. Mash a few beans against the pot with a spoon if a slightly fuller broth is desired.
Stir in spinach and cook for 2 minutes until wilted.
Remove from the heat and stir in Parmesan until dispersed, then serve with the beans and chicken evenly divided.