In a large pot, heat the oil over medium heat. Add the onion and cook, stirring occasionally, until soft, about 5 minutes. Increase the heat to medium-high and add the squash, chipotle chile, adobo sauce and brown sugar; cook, stirring, for 5 minutes. Pour in the vegetable broth and bring to a boil. Lower the heat and simmer, covered, until the squash is cooked through, about 20 minutes. Remove from the heat and stir in the mangoes.
Using a blender, puree the soup. Stir in the buttermilk and season with salt and pepper. Warm over low heat. Sprinkle with the chives and coarsely ground pepper.