In a large saucepan, sweat leeks and a pinch of salt in butter over medium heat until wilted, but not colored.
Add potatoes and stock. Bring to a boil, then reduce heat to a simmer and cook, covered, until potatoes are very soft, about 45 minutes.
Puree soup with an immersion blender, or in batches in a blender or food processor. Return to saucepan over very low heat.
Add cream, milk and yogurt, whisking to combine.
Taste. Season with salt and white pepper as desired. Black pepper can be used, but will have a milder effect, and will be visible in the finished soup.
Serve warm or chilled, garnished with herbs of choice.
Store in a covered container, refrigerated for up to 1 week, or in single servings in containers or freezer bags for up to 6 months.