In a large bowl, combine egg, bread crumbs, half of the thyme and salt. Crumble beef over mixture and mix well. Shape into 1-in. balls. In a Dutch oven or soup kettle, brown meatballs; drain and set aside.
In the same pan, saute onion, carrots and mushrooms in oil until onion is tender. Stir in the potatoes, broth, tomatoes, meatballs and remaining thyme. Bring to a boil. Reduce heat; cover and simmer for 25-30 minutes or until potatoes are tender.