Heat the oil or butter in a large pan over medium heat. Add the chopped onion and sliced leeks and cook gently for 5 minutes until soft but not browned.
Add the diced potatoes and stir to coat them in the oil. Pour in the vegetable stock, season with salt and pepper, and bring to a simmer.
Cover and simmer for 15-20 minutes until the potatoes are completely soft when pressed against the side of the pan with a spoon.
Blend the soup with a stick blender or in a food processor until completely smooth. If it seems too thick, add a splash of boiling water.
Stir in the grated cheddar a handful at a time, letting each handful melt before adding the next. Taste and adjust the seasoning, add a pinch of nutmeg if you have some.
Serve hot with bread on the side. The cheese makes it rich enough that you do not need cream.