Evenly slice the leeks (about 1 cm/½ in thick) and then wash them, using a colander under cold running water. Set aside.
Add the unsalted butter to a saucepan and place over a low heat.
Evenly dice the onion and add to the pan. Allow the onion to sweat until cooked, ensuring that the onions don't colour.
Add the sliced leeks to the pan with the onion and continue to cook gently for about 5–7 minutes, stirring occasionally, until the leeks have softened.
Add the vegetable stock to the pan and simmer for 10 minutes.
Add the double cream to the pan and bring to the boil. Remove from the heat.
Use a stick blender to combine the ingredients into a soup-like texture. Season with sea salt and pepper to your taste.
To make the chive oil, combine the chives and vegetable oil in a food blender and blend until smooth.
Using a sieve and cheese cloth positioned over a bowl, pour the contents of the blender over the cloth and allow the oil to pass through.
Garnish the soup with the chive oil and serve.