Bring chicken broth to a boil. Add potatoes. Lower heat to simmer. Add minced garlic and black pepper and cook for 30 minutes.
Add spring garlic and heavy cream and cook for an additional 10 to 15 minutes. In a small bowl, mix cornstarch and water together to make a slurry. Slowly pour the slurry into the soup, and bring to a boil to thicken. Thickness of the soup will depend on starchiness of potato. When soup reaches desired thickness, add cheese. Thoroughly melt cheese and serve.