Brown the meat with the onion, celery, and garlic in a large pot over medium-high heat. Remove the pot from the heat and drain off as much fat as you can. (Discard the fat once it cools.)
Return the pot to the heat and add the rest of the ingredients: whole tomatoes, beef stock or broth, bell peppers, carrots, red potatoes, tomato paste, salt, pepper, and spices. Stir to combine, then bring to a boil. Reduce the heat, then cover the pot and simmer the soup for 15 to 20 minutes more, until potatoes are tender but not overly mushy.
Taste and adjust the seasonings, adding more salt if needed.