To prepare the leeks, cut off the root end and dark green parts. For the white and light green part, cut in half lengthwise and then cut across into fairly thin strips.
In a large pot or saucepan, add the butter and melt over medium heat. Once the butter has melted, add the onions and sweat for about 5 minutes until they start to soften. Next, add the garlic and cook for another minute or so. Add the leeks and salt and stir. Cover with a lid and let sweat over medium heat for about 8 minutes or until the leeks soften. Stir occasionally.
Peel, quarter the potatoes lengthwise and finely slice. Add the potatoes and stir to combine.
Add hot stock (more or less) to just to cover the ingredients. Bring the soup to a simmer. Cover and let cook over medium-low heat for about 10 minutes or just until the potatoes have just cooked through.
Season to taste.
Garnish the soup with chives and a drizzle of heavy cream.