Cut the leeks in half lengthways and slice the leeks and celery in 1 cm chunks. Set aside the celery fronds for garnish.
Peel and dice the potatoes into 1 cm pieces.
Heat the butter and oil over a medium heat and add the leeks and celery.
Cook, stirring occasionally, for 10 minutes until the vegetables are soft.
Add the potatoes, rice, stock and seasoning.
Bring the mixture to a boil and put the lid on the pot.
Simmer for 20 minutes until the rice is cooked and the potatoes are tender.
Use a stick or immersion blender to blend the soup until it is smooth.
Stir in the milk and reheat the soup.
Garnish the soup with a drizzle of cream, the chopped celery fronds, a grind of black pepper and some croutons.