Add the finely chopped onion and minced garlic to the pot. Gently sauté them for approximately 3 to 4 minutes until they turn translucent.

Next, add in the thinly sliced leeks and the diced potatoes. Continue cooking for an additional 5 minutes, occasionally giving it a gentle stir.

Now, pour the vegetable stock into the pot and bring the mixture to a vigorous boil. Once boiling, lower the heat, cover the pot, and allow it to simmer for approximately 20 to 25 minutes or until the potatoes have reached a tender state.

With care, use an immersion blender to achieve a smooth and creamy consistency for the soup.

Return the soup to the stove and gently incorporate the single cream, making sure not to bring it to a boil.

Season the soup to your liking with salt and freshly ground black pepper.

Serve the steaming hot soup, garnished with freshly chopped chives.