In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion and garlic, sautéing until the onion is translucent (about 3-4 minutes).
Add the ground beef to the pot and cook until browned, breaking it apart with a wooden spoon as it cooks (about 5-7 minutes). Drain excess fat if necessary.
Stir in the chopped carrots, celery, and bell pepper, cooking for an additional 5 minutes until slightly softened.
Pour in the beef broth and stir in the diced tomatoes, green beans, dried basil, and dried oregano. Season with salt and pepper to taste.
Bring the soup to a boil, then reduce the heat to low and let it simmer for 20 minutes. Stir occasionally to prevent sticking.
Taste and adjust the seasoning as needed. If desired, simmer for longer to develop more flavor.
Remove from heat and ladle the soup into bowls. Serve hot.