Prepare the Vegetables: Start by thoroughly washing the celery, carrots, and cabbage. Chop the celery stalks and carrots into uniform pieces to ensure even cooking. Dice the onions and green bell peppers, and set everything aside.

Chop the Cabbage: Remove any wilted outer leaves from the cabbage and chop it into manageable chunks. For a finer texture, you can slice the cabbage more thinly.

Assemble in a Pot: Place a large stockpot on the stove over medium heat. Add the chopped celery, carrots, onions, green bell peppers, and cabbage. Pour in the drained green beans and spread the vegetables evenly in the pot.

Add the Liquids: Pour the two quarts of tomato juice over the vegetables, followed by the cans of whole peeled tomatoes with their liquid. Crush the whole tomatoes gently with your hands or a spoon to break them up slightly.

Incorporate Broth and Seasoning: Add the beef broth and sprinkle the dry onion soup mix over the top. This step infuses the soup with a robust, savory base.

Add Water and Simmer: Pour cold water into the pot until it covers the vegetables and reaches about 1 inch below the rim. Stir to combine all the ingredients.

Cook the Soup: Bring the mixture to a boil. Once boiling, reduce the heat to low, cover the pot with a lid, and let it simmer for about 1 hour. Stir occasionally to ensure even cooking.

Taste and Adjust: After an hour, check the seasoning. Add salt and pepper to taste if needed.

Serve: Ladle the hot soup into bowls and enjoy it on its own or with a slice of crusty bread for an extra touch of comfort.