Melt the butter in a large saucepan over medium-low heat. Add the scallions and cook 1 minute. Add the potatoes, wine, cream, broth, salt, and 1/4 teaspoon of the pepper and bring to a boil. Reduce heat and simmer until the potatoes are tender, about 15 minutes. Ladle the soup into individual bowls and sprinkle with the remaining pepper.
Tip: Add flavor and texture by stirring in 1 cup frozen corn kernels during the last 5 minutes of cooking.