Melt butter in soup pot over medium-high heat. Add leeks and salt; cook until leeks begin to wilt. Reduce heat to medium or medium-low and cook until soft and almost pastelike, 30 to 40 minutes.
Place potatoes in the pot; add chicken broth. Adjust heat so mixture simmers slowly. Cook until potatoes are soft, about 30 minutes. Puree mixture with an immersion blender or in batches in a blender. Whisk in heavy cream and creme fraiche. Heat over medium heat. Add more salt, if needed, and cayenne pepper. Do not boil.
Serve with a drizzle of creme fraiche and a sprinkle of chopped chives.
