Heat a large pot or Dutch oven over medium-high heat. Crumble the ground chuck (2 pounds) into large chunks in the hot pan, and cook until evenly browned. Transfer cooked beef to a paper towel-lined plate. Discard all but 2 tablespoons of drippings from the pot. If you do not have that amount remaining, add vegetable oil to make up the difference.
    Add the onion (1), garlic (3 cloves), and carrots (4) and saute, over medium heat, until soft, about 5-6 minutes.
    Sprinkle flour (3 tablespoons) 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 stock (3 cups), stewed tomatoes with their juices (2 (14.5-ounces) cans), tomato soup (1 (10.75 -ounce) can), Better Than Bouillon (1 heaping tablespoon), Worcestershire sauce (2 tablespoons), potatoes (3), Italian seasoning (1 teaspoon), thyme (1/4 teaspoon), bay leaf (1), salt (2 1/4 teaspoons), pepper (1 teaspoon), green beans (1 1/2 cups), pearl onions (1 cup), and browned beef; stir to blend then simmer over low heat for at least 2 hours, stirring occasionally.
    Adjust seasoning. Ladle into individual bowls and serve.