Preheat the oven to 200oC, gas mark 6. Line a small baking tray with baking parchment.
Heat 1 tbsp oil in a large frying pan and fry the leeks and potatoes for 5 minutes, stirring occasionally. Add the stock and herbs and bring to the boil, cover and simmer for 10 minutes until potatoes are tender.
Meanwhile, place half the walnuts on the prepared tray and toss in 1 tsp oil, sprinkle over the Parmesan and bake for 5 minutes, allow to cool on the tray.
Puree the soup with a stick blender so that the texture is still quite chunky. Chop the remaining walnuts and add to the soup, season to taste.
Serve the soup with broken up pieces of the Parmesan walnuts on top.
Notes
Cooks tip Try adding some pan fried diced pancetta or chopped bacon.