Stir the sour cream and chile pepper in a small bowl.
Heat the oil in a 6-quart sauce pot over medium heat. Add the onion and cook for 4 minutes. Add the garlic and cook for 30 seconds. Stir the broth, cilantro, lime juice and avocados in the sauce pot. Heat to a boil.
Place 1/2 of the avocado mixture in a blender or food processor. Cover and blend until smooth. Pour the mixture into a medium bowl. Repeat the blending process with the remaining avocado mixture. Return all of the puréed mixture to the sauce pot. Cook over medium heat until the mixture is hot. Divide the soup among 8 serving bowls. Top each with about 1 tablespoon of the sour cream mixture.