Brown the beef: Heat a large pot or Dutch oven over medium-high heat. Add the ground beef and cook, breaking it up with a spoon, until browned and no longer pink, about 5–7 minutes.
If there’s excess fat, drain it, leaving about 1 tablespoon in the pot.
Sauté aromatics: If the pot looks dry, add the olive oil. Stir in the onion, carrots, and celery with a pinch of salt. Cook until the onion softens, about 4–5 minutes.
Add the garlic and cook for 30 seconds, stirring.
Build the base: Stir in the tomato paste and cook for 1 minute to caramelize it slightly. Add the smoked paprika, Italian seasoning, and a few grinds of black pepper. Mix well.
Deglaze and simmer: Pour in the beef broth and scrape up any browned bits from the bottom of the pot.
Add the diced tomatoes with their juices, Worcestershire sauce, bay leaf, potatoes, and green beans. Stir to combine.
Cook until tender: Bring the soup to a gentle boil, then reduce to a simmer. Cook uncovered for 20–25 minutes, or until the potatoes and carrots are tender but not falling apart.
Taste and season with salt and more pepper as needed.
Finish and serve: Remove the bay leaf. Ladle into bowls and top with chopped parsley. Serve with crusty bread or a side salad.