1. Light the grill. In a small bowl, combine 3 tablespoons of the oil with the cayenne, thyme, nutmeg, brown sugar, vinegar, 3/4 teaspoon of the salt, and 1/4 teaspoon black pepper. Rub the mixture over the pork.
2. Bring a medium pot of water to a boil. Add the sweet potatoes and cook until almost tender, about 5 minutes. Drain. Brush the sweet potatoes and the scallions with the remaining 2 tablespoons oil and sprinkle with the remaining 1/4 teaspoon salt and 1/8 teaspoon pepper.
3. Grill the pork over moderate heat, turning once, until done to medium, 12 to 15 minutes in all. Transfer the pork to a carving board and leave to rest in a warm spot.
4. Grill the sweet potatoes and scallions, turning, until tender, about 5 minutes. Cut the pork into 1/2-inch diagonal slices. Serve with the vegetables.
Variation: Substitute 1 pound of asparagus spears for the scallions. Snap off the tough ends and use an additional tablespoon of oil for brushing the spears. Grill for about 10 minutes.
Wine Recommendation: Australian Shiraz's lush, jammy fruit flavor makes it a great partner for grilled meats. Try one here for an inexpensive but tasty treat.