Melt butter in a large heavy saucepan over medium heat.
Add leeks, parsnips, salt & pepper.
Cook, stirring often, until softened but not browned, about 10 minutes.
Pour in 4 cups broth, increase heat to high and bring to a full boil.
Reduce heat to medium-low and cook partially covered, stirring occasionally, until veggies are very soft, about 30 minutes.
Let cool slightly.
Working in batches, puree soup in a blender.
Return soup to saucepan and stir in cream.
Warm over low heat and season well with salt and pepper.
Thin with remaining broth if soup is too thick.
Ladle into warmed soup bowls.
Garnish with a swirl of heavy cream & a pinch of chives and serve.