Heat oil in a large stockpot over medium heat. Add onions or leeks, celery, and Italian seasoning; season with salt and pepper. Cook, stirring frequently, until onions are translucent, 5 to 8 minutes.
Add broth, tomatoes and their juice, tomato paste, and 3 cups water to pot; bring mixture to a boil. Reduce heat to a simmer, and cook, uncovered, 20 minutes.
Add vegetables to pot, and return to a simmer. Cook, uncovered, until vegetables are tender, 20 to 25 minutes. Season with salt and pepper, as desired. Let cool before storing.