Heat the butter and oil together in a large saucepan, over a medium heat.
Finely chop the banana shallots, and then toss them into the hot fat, stirring occasionally.
Prepare the leeks by cutting off the leaves, and any dark green parts of the stalk.
Split the leeks into halves and then quarters lengthways, and then finely chop.
Toss the leeks on top of the onions and give everything a good stir.
Rinse off the potatoes, then chop them into a 1cm dice. I see no need to peel the potatoes, although if you want to remove the skins, you are welcome to do so.
Add the potato to the saucepan, and stir everything together again.
Stir the vegetables ocassionally until the potatoes have started to soften - about 5 minutes.
Add the chicken stock to the saucepan, and then bring everything to the boil.
Reduce the heat to a gentle bubble, then place on the lid and simmer for about 10 minutes, until the potato is soft through.
Use an immersion blender to blitz the soup. You could also use a food processor, or regular blender.
Season the soup with plenty of salt and a little pepper.
Garnish with a splash of cream, and some finely chopped chives.