How to Make It
Place leeks, shallots, and oil in a Dutch oven over medium-low. Cover and cook, stirring occasionally, until vegetables are soft but not brown, 10 to 12 minutes.
Add potatoes, stock, and bay leaves; bring to a boil over high. Reduce heat to medium, and cook until potatoes are tender, 10 to 12 minutes. Discard bay leaves.
Scoop 5 cups of hot soup into a blender. Remove center piece of blender lid (to allow steam to escape); secure lid on blender, and place a clean towel over opening in lid. Process until smooth, about 1 minute; transfer to a large bowl. Repeat process with remaining soup. Stir in cream, vinegar, salt, and pepper. Chill at least 3 hours or overnight. Sprinkle each serving with chives and pepper.