Using paper towels, pat beef dry (you need the meat dry to get a nice sear) and season with salt and pepper. Heat large pan over medium-high heat with 1 tablespoon oil until just smoking. Brown half of meat, about 6-8 minutes. Transfer meat and juices to slow cooker insert, and repeat with 1 tablespoon oil and rest of meat.
Keep heat at medium-high, add 1 tablespoon oil to pan, onions, fennel, mushrooms, and carrots. Cook, stirring often, until mushrooms have released their moisture and vegetables are softened, about 7-8 minutes. Add garlic and cook until fragrant, about 1 minute. Transfer vegetables to slow cooker insert.
Add wine, broth, tomatoes, barley, tomato paste, and thyme to slow cooker insert. Cover slow cooker and cook until meat is tender; LOW for 8 hours or HIGH for 4-5 hours. 10 minutes before serving, ladle off fat from surface, and stir in Worcestershire sauce and parsley. Cover and cook 10 more minutes. Season to taste with salt and pepper. Ladle soup into bowls, and garnish with parsley, serve.