Peel and chop the beetroot. Finely chop the onion and thinly slice the cabbage.
Heat the oil in a large saucepan and gently fry the onion for 5 minutes. Add the beetroot and cook for 5 minutes, while stirring.
Add the thyme and caraway seeds and stir for a minute. Add the cabbage, stir for a few seconds, then add the stock. Bring to a simmer, then gently cook gently for 15 minutes.
Stir in the chestnuts and cook for another 5 minutes or so.
When the vegetables are tender, turn off the heat and blitz with a stick blender until you get a smooth or textured soup (to your liking).
Serve with chestnuts crumbled on top or, for a non-vegan version, with a dollop of crème fraîche mixed with chopped dill or chives.