Rub corn, peppers, green onions, and jalapeño lightly with oil. Place on a grill over a bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds); close lid on gas grill. Cook, turning occasionally, until slightly charred, about 5 minutes total for green onions and jalapeño, 10 to 12 minutes total for other vegetables. Let cool. Cut corn kernels from cobs; chop peppers, green onions, and jalapeño.
In a blender, whirl 1/2 the broth and corn and the sour cream, cilantro, cumin, green onions, and jalapeño until smooth. Pour into a bowl. Stir in remaining broth and corn, the lime juice and peppers, and salt and pepper to taste. Chill until cold, 1 hour or up to 1 day. Just before serving, pit, peel, and dice avocado; ladle soup into bowls and top with avocado.