Start by heating a large soup pot over medium-high heat. Add the ground beef or lamb and cook until browned, breaking it apart with a spoon as it cooks. Once fully cooked, transfer the meat to a plate and drain excess grease if needed.
Add butter to the same pot and stir in the chopped onions. Cook until softened and lightly golden, then add the garlic and Italian seasoning. Stir for about a minute until fragrant and flavorful.
Mix in the tomato paste and cook briefly to deepen its flavor. Pour in the beef broth, Worcestershire sauce, heavy cream, and diced potatoes. Return the cooked meat to the pot and stir everything together.
Bring the soup to a gentle boil, then reduce the heat to simmer. Let it cook uncovered for about 20 minutes or until the potatoes become soft. Stir occasionally so nothing sticks to the bottom.
Use a potato masher to mash some of the potatoes directly in the pot. This naturally thickens the soup while still leaving chunks of potato for texture. Add the cornstarch slurry and stir well.
Stir in the frozen mixed vegetables and continue simmering for another 10 to 15 minutes. The vegetables should become tender while the broth thickens slightly. Taste and season generously with salt and pepper.
Ladle the hot soup into bowls and sprinkle fresh parsley on top. Serve immediately while warm and creamy. Pair it with crusty bread for the ultimate comfort meal.