Preheat oven to 400deg. Bake potatoes on the floor of the oven, turning once, for 1 hour or until they are soft when pressed. Cut the cooked potatoes in half and scoop out the flesh.
Cut leeks in half lengthwise, wash throughly to get out all sand and grit and chop coarsely.
In a large saucepan, bring the broth to a boil over moderately high heat. Add the chopped leeks and white pepper, reduce heat and simmer the leeks, covered for 30 minutes or until they are very tender.
Add the potato flesh to the leeks and puree the mixture in batches in a food processor until very smooth. Transfer the puree to a mixing bowl, add salt if desired and chill covered for at least 2 hours or up to 24 hours.
Whisk in the yogurt or milk and chill again for 30 minutes if necessary.
Ladle the soup into bowls and top each serving with 1-1/2-2teaspoons of red caviar and sprinkle with chives.
Serve in chilled bowls.