Preheat an indoor or outdoor grill.
Cut the large potatoes into thirds (rounds about 1/2-inch thick), then cut the medium potatoes in half. Small potatoes you can leave whole. Season the potatoes and scallions with EVOO, salt and freshly ground black pepper. Place the potatoes and scallions on the grill and tent with one large piece of tin foil. Cook the scallions until they are charred slightly, about 7 minutes, then remove them to a large mixing bowl to cool. Once the scallions come off, turn the potatoes and cook 7-10 more minutes, until tender.