Sauté the onion in a large non-stick pan until soft, using a little water to stop the onion catching (5 – 10 minutes depending on how finely you have chopped them).
Add the chestnuts, vegetable stock and rosemary. Bring to a simmer and simmer for 15 minutes.
Take off the heat, add the milk and then using a stick-blender or high-speed blender, process until completely smooth.
Transfer back to the pan and if you think it is too thick, let it down a little with water from a recently boiled kettle, until you have the consistency you want. Taste and season to your liking with sea salt and black pepper.
Serve with warm crusty bread in hot soup bowls, drizzled with a little extra virgin olive oil if you like.
Options and Extras
Red onions can be used instead of shallots.
This soup is also lovely served with some roughly chopped mushrooms, sautéed in a dry non-stick frying pan until they start to soften and brown. Season before spooning over the soup in each bowl.