Trim the roots and top 3cm off the leek. Halve it, rinse out any grit and finely slice it. Warm a large pan over a medium-low heat for 1 min, then add 1 tbsp oil, the leek and a pinch of salt and pepper. Cook, stirring occasionally, for 8 mins till the leek is soft but not too browned. If it starts to colour, turn the heat down.
While the leek cooks, peel and chop the potatoes into small cubes, around 1cm across. Finely chop the parsley stalks and half the leaves. Keep the rest of the leaves for later.
Stir the potatoes and chopped parsley stalks and leaves into the leek with 2 tbsp water. Pop on a lid. Cook, stirring a few times, for 5 mins till the potatoes have just softened.
Drop the bay leaf into the pan. Crumble in the stock cube and pour in 700ml boiling water. Pop a lid on the pan, turn the heat up and bring to the boil. When the soup is boiling, turn the heat down and simmer for 15 mins till the potatoes are soft.
While the soup simmers, separate the spring green leaves and finely slice them. When the soup has simmered for 15 mins, add the spring greens. Simmer, without the lid on the pan, for 5 mins till the spring greens are just tender. Lift out the bay leaf and discard it.
Ladle the soup into a blender and whizz a few times to just combine everything, or use a hand-held blender in the pan. Taste and add more salt and pepper if you think it needs it. Ladle into warm bowls and garnish with the last of the parsley leaves to serve.