In a large mixing bowl, combine ground beef or turkey, breadcrumbs, grated Parmesan cheese, large egg, minced garlic, dried Italian herbs, salt, and black pepper. Mix everything thoroughly until well combined.

Roll the meat mixture into small meatballs, each about 1 inch in diameter. Place them on a plate or baking sheet, allowing them to rest.

In a large pot or Dutch oven, heat a drizzle of olive oil over medium-high heat. Carefully add the formed meatballs and brown them on all sides for about 5-7 minutes. Remove and set aside.

Without cleaning the pot, add diced carrots, diced celery, and diced potatoes. Sauté for about 5 minutes over medium heat until softened.

Pour in chicken or vegetable broth, stirring well. Bring to a boil, then reduce heat and let it simmer for 10 minutes.

Return the browned meatballs to the pot and stir them into the broth. Then pour in the heavy cream, mixing until the soup achieves a creamy consistency. Simmer for an additional 10-15 minutes.

Taste the Italian Meatball Soup and adjust seasoning with additional salt and pepper as needed. Ladle into bowls and sprinkle chopped fresh parsley on top.