Use curly parsley, chop parsley roughly including any stalks.
Melt butter in a pan and add the parsley and chopped leeks.
Sweat the vegetables.
Add cut, boiled potatoes to thicken the soup.
Add chicken stock.
As the soup is cooking, make the chive cream:-
Chop chives, and add to cream.
Back to the soup - just before it's liquidised, throw in any remaining parsley (it keeps keep the fresh green colour to the soup) in the last minute of cooking and liquidize the soup in a food processor.
Back into the pan, add double cream, salt and black pepper.
Serve with a spoon of chives-cream in the soup.