Preheat the oven to 425 degrees F. Peel and dice 2 1/2 sweet potatoes. Melt 2 tablespoons butter in a large pot over medium heat. Add the onion and garlic and cook until soft, about 5 minutes. Stir in the ginger, nutmeg, 1 1/4 teaspoons curry powder, and salt and pepper to taste and cook until toasted, 1 more minute.
Add the diced sweet potatoes, chicken broth and 2 cups water to the pot, cover and bring to a boil over medium-high heat. Reduce the heat to medium low and stir in the applesauce. Simmer, covered, until the sweet potatoes are soft, about 20 minutes. Puree the soup with a blender until smooth. Season with salt and pepper; keep warm.
Meanwhile, peel and thinly slice the remaining 1/2 sweet potato and toss with the olive oil, and salt and pepper to taste. Spread in a single layer on a baking sheet and bake until crisp, 7 to 10 minutes.
Heat the remaining 1 tablespoon butter in a skillet over medium heat. Add the remaining 1/4 teaspoon curry powder and cook, stirring, until browned; remove from the heat and add the vinegar. Top with the curry butter, cilantro and sweet-potato chips.