Halve, pit, and peel avocados.

In a blender or food processor, combine avocados, lemon or lime juice, chicken broth, buttermilk, 2 cups ice water, cumin, Tabasco, salt, and pepper.

Blend until smooth.

Transfer the soup to a large bowl.

Thin with remaining ice water to desired consistency.

Chill, covered, for at least 2 hours and up to 4 hours.

For the Chili Coriander Cream, in a blender or small food processor, combine sour cream, plain yogurt, chopped garlic, seeded and chopped jalapeno, and chopped fresh coriander.

Add salt and pepper to taste.

Blend until very smooth, scraping down sides as needed.

Chill the cream for up to 6 hours ahead of time.

Serve the soup with Chili Coriander Cream and coriander sprigs.