Start by heating a tablespoon of olive oil in a large pot or Dutch oven over medium heat. Add the ground beef and cook until it’s browned and no longer pink, breaking it apart as it cooks. Once browned, remove any excess fat if needed. Next, stir in the diced onion, celery, green bell pepper, and minced garlic. Let these sauté for about 5 minutes until fragrant and slightly softened.
Add the tomato paste and stir it into the vegetables and beef, allowing it to cook for about 2 minutes to deepen its flavor. Then, place the smoked turkey leg into the pot and pour in the beef or chicken broth, scraping any browned bits off the bottom of the pot. Stir in the diced tomatoes (with their juices), Worcestershire sauce, and season with Italian seasoning, bay leaf, thyme bundle, black pepper, and salt to taste.
Bring the pot to a gentle boil, then reduce the heat and let it simmer uncovered for about 25–30 minutes. Add the diced Yukon gold potatoes and mixed frozen vegetables during the last 15 minutes of cooking. Simmer until the potatoes are fork-tender and the soup is well blended. Remove the smoked turkey leg, shred the meat, and return it to the pot. Discard the bone and bay leaf. Garnish with fresh chopped parsley just before serving.