Heat a dutch oven over medium high heat. Add the olive oil and heat until it shimmers. Add the ground beef and sautee, stirring frequently to break into pieces, until browned and no longer pink, 6-7 minutes
Add the onion to the beef and saute until soft, stirring occasionally, 6-7 minutes. Add the garlic and cook, stirring continuously, for 1 minute more.
Add the tomato paste and work into the beef and onions; cook until the color deepens, about 2 minutes.
Add the carrot, celery, and bell pepper, then top with the pureed tomatoes, beef broth, salt, pepper, and italian seasoning. Give the soup a good stir, then top with a bay leaf.
Increase the heat to high and bring the soup to a boil. Reduce heat to a simmer.
Add the green beans, and stir into the soup. Simmer an additional 5 minutes until the green beans are cooked through.
Taste for seasoning and add additional salt and pepper if needed. Ladle into soup bowls and serve immediately.