Sauté the leeks: In a large pot, heat olive oil over medium heat. Add the sliced leeks and cook for 5-7 minutes until soft and translucent.

Add potatoes and broth: Once leeks are softened, add diced potatoes and vegetable broth, bring to a boil then simmer covered for 20 minutes until potatoes are tender.

Purée the soup: Carefully use an immersion blender to purée the soup until smooth, stir in heavy cream, and season with salt and pepper.

Final simmer: Let the soup simmer on low heat for another 5-10 minutes to meld flavors.

Prepare chive oil: Blend fresh chives with olive oil in a processor until finely chopped, then strain for a smooth chive oil.

Serve the soup: Ladle the soup into bowls and drizzle the chive oil on top, serve warm, optionally with crusty bread.