Heat a large pot over medium-high heat. Crumble the ground chuck into large chunks in the hot pan, and cook until evenly browned. Discard all but 2 tablespoons of drippings from pot. If you do not have that amount remaining, add vegetable oil to make up the difference.
Add the onion, garlic, and carrots and saute, over medium heat, until soft, about 5-6 minutes.
Sprinkle flour over vegetables, stirring constantly, until the flour coats the vegetables. Cook for 2-3 minutes to toast the flour. Remove skillet from heat.
Add beef broth, stewed tomatoes with their juices, tomato soup, Better Than Bouillon, Worcestershire sauce, potatoes, Italian seasoning, thyme, bay leaf, salt, pepper, green beans, pearl onions, and browned beef; stir to blend then simmer over low heat for at least 2 hours, stirring occasionally.
Adjust seasoning. Ladle into bowls and top with cheese. Serve.