Heat the olive oil in a 4- to 6-quart Dutch oven over medium-high heat. Add the beef chuck in 2 batches and cook, stirring occasionally, until the meat is nicely browned, about 7 minutes. Season the beef with the salt.
Add the onion, carrots, celery and garlic and cook, stirring, for 5 minutes. Pour in the beef broth and tomatoes and bring to a boil. Reduce the heat and simmer for 15 minutes.
Add the potato, green beans, white beans and Worcestershire sauce and simmer until the beef and vegetables are tender, about 30 minutes.
Spoon the minestrone into mugs and garnish with celery ribs and chopped parsley. Serve with horseradish, lemons and hot sauce.