In a blender jar, combine avocado, green onion, lemon juice, cilantro and white pepper. Add 1 cup of the broth; cover and blend until smooth. Add remaining broth and blend 1 minute longer. Chill 30 to 60 minutes. Blend briefly before serving. Garnish each serving with 1 or 2 thin slices of avocado and sprig of cilantro, if desired. Serving Suggestions: Can be served in hollowed-out avocado half-shells. Scoop avocado from shells with spoon instead of peeling and cubing avocado. Use remaining avocado in Guacamole or tossed Salads.