In a large bowl, toss the beef cubes with flour, salt, and pepper until evenly coated.
Heat 2 tablespoons of olive oil in a large skillet or Dutch oven over medium-high heat. Add half of the beef in a single layer and sear for 3-4 minutes per side, until well browned. Transfer the seared beef to a 6-quart or larger slow cooker. Repeat with the remaining beef, adding the last tablespoon of oil if needed.
Reduce the skillet heat to medium. Add the minced garlic and cook for 30-60 seconds until fragrant. Pour in the red wine to deglaze, scraping the bottom of the pan to release any browned bits. Let it bubble for 1-2 minutes.
Pour the wine reduction from the skillet into the slow cooker. Add the onion, carrots, celery, potatoes, diced tomatoes, beef broth, tomato paste, Worcestershire sauce, and Italian seasoning. Stir everything to combine.
Nestle the bay leaves and thyme sprig into the soup. Secure the lid on the slow cooker.
Cook on low for 7-8 hours or on high for 5-6 hours, until the beef is tender.
About 1 hour before the cooking time is complete, stir in the fresh green beans. Cover and continue cooking.
Before serving, remove and discard the bay leaves and thyme sprig. Taste the soup and add more salt and pepper if desired. For safety, ensure the beef is tender and has reached an internal temperature of 145°F (63°C), followed by a three-minute rest.
Ladle the soup into bowls and serve warm.