Chilled Corn and Buttermilk Soup

Cut corn kernels off cobs; transfer kernels to large bowl. Scrape cobs over bowl with knife to remove any remaining bits of corn and milky liquid. Break cobs in half crosswise and reserve. Heat oil in heavy large saucepan over medium-high heat. Add shallots, ginger, and garlic; sauté until shallots begin to soften, about 2 minutes. Add corn and any accumulated liquid in bowl. Cook until heated through, stirring occasionally, about 3 minutes. Add cobs and broth. Bring soup to boil; reduce heat to low, cover pan, and simmer until corn is very tender, about 30 minutes. Discard cobs. Working in batches, puree soup in blender. Transfer to large bowl. Stir 1 cup buttermilk into soup. Cover and refrigerate until chilled, at least 3 hours. (Can be made 1 day ahead. Keep chilled.) Season soup to taste with salt and pepper. Divide soup among 8 bowls. Drizzle with additional buttermilk, sprinkle with chives, and serve.