Soften the leeks: Heat butter and olive oil in a large saucepan over low heat.Add leeks and cook gently for 8–10 minutes, stirring, until soft but not browned.
Add potatoes and stock: Stir in diced potatoes and pour in the stock. Bring to a gentle boil.
Simmer: Reduce heat and simmer for 20 minutes, until potatoes are very tender.
Blend the soup: Use a stick blender or blender to puree until smooth and creamy.
Add milk and season: Stir in milk or cream. Season with salt and black pepper to taste.
Reheat gently: Warm through without boiling.
Serve: Ladle into bowls and garnish with chives or parsley.