Coarsely chop the avocado and place in a medium bowl with 4 tablespoons of sour cream. Mash the avocado and combine with the sour cream. Warm the chicken stock in a pan. When hot, but still below simmering, stir in the remaining sour cream. Gradually stir the avocado mixture into the pan. Heat, but do not let the mixture approach boiling. Using an immersion blender or standard blender, in smaller batches, blend the soup. Ladle the soup into bowls and sprinkle with cilantro and black pepper.