Clean and chop carrot, celery, and onion. Place in pot with olive oil and sauté for 5 min. Do not burn.
Add ham and continue to cook ~5 more minutes. Fat from smoked ham should be released from meat. For ground beef, add salt and pepper. Skip for vegetarian meal.
Add broth, water (using broth can), diced tomatoes, and tomato sauce. Stir.
Measure and add vegetables and ditalini pasta. Salt and pepper to taste.
Bring soup to a boil. Place lid on pot and reduce to Medium temperature - being careful to not let soup boil over. Cook for 20 minutes.
Optional: Simmer on Low for an additional 15 minutes.
Serve with toasted sourdough bread, grilled cheese, or corn bread.