Heat the oil in a large pot over medium to medium-high heat until hot but not smoking. Add the ground beef and sprinkle with the salt. Stir well, then arrange it in one layer. Cook for 3 minutes without disturbing.
Stir the beef and continue cooking for 2 minutes (or until browned). Break up large pieces while stirring. If necessary, drain some or most of the oil rendered (see note 2).
Lower the heat to medium and add the onions, carrots, and celery to the pot. Cook for 3 minutes, stir often.
Next, add the garlic, Italian seasoning, and black pepper. Cook for 1 minute, stirring frequently.
Add the diced tomatoes and beef broth. Stir while gently scraping any bits off the bottom of the pot. Raise the heat to high and bring the broth to a boil (it will take about 3-4 minutes).
Once the broth is boiling, lower the heat to medium-low, cover the pot and simmer the soup for 10 minutes to let the flavors come together (see note 3).
Add the potatoes and the chopped cabbage.
Raise the heat to high and bring to a boil (will take about 3-4 minutes). Then, lower the heat to medium-low, cover and cook for about 20 minutes or until the potatoes and cabbage are tender. Stir occasionally and keep the soup at a simmer. Raise or lower the heat as needed.
Taste the soup and add salt, if needed. As a reference we added ½ teaspoon to ours. Serve and garnish with chopped parsley, if desired.