1. Melt butter in a medium pan over medium heat.
2. Add minced shallots and minced ginger; sauté for about 1 minute.
3. Add chicken broth, lime juice, cayenne pepper; bring to a boil.
4. Reduce heat to medium-low and simmer for about 3 minutes.
5. Transfer mixture to a large bow.
6. Purée avocados and half & half in a blender.
7. Whisk into soup.
8. Season with salt and pepper.
9. Cover and refrigerate for at least 3 hours.
10. Garnish soup with cilantro and lime slices.