Trim the roots and the tough dark green tops from the Leeks, slice the white and pale green parts thinly, then rinse thoroughly to remove any grit.
Peel and cut the Potatoes into roughly 1-inch chunks so they cook evenly.
Place the sliced leeks and potato chunks in a large saucepan and add enough Water to cover them by about 1–2 inches.
Bring to a boil over medium-high heat, then reduce to a simmer and cook until the potatoes are very tender, about 15–20 minutes.
Using an immersion blender (or transfer in batches to a blender), purée the soup until smooth and velvety; return to low heat if needed.
Stir in the Heavy Cream and season with Salt to taste; warm gently without boiling so the cream stays silky.
Ladle the potage into bowls and sprinkle with finely chopped Chives for a fresh, oniony finish. Serve hot.
