Heat the oil in a large pan over medium heat. Add the onion, turn the heat down to low and cook gently, stirring occasionally, for about 5 minutes, until softened but not brown.
Add the beetroot, carrot and half the thyme. Turn the heat up to medium and cook, stirring, for 2 minutes to allow the vegetables to caramelize slightly.
Add the vinegar, stock and horseradish, and bring up to the boil. Once boiling, turn down the heat slightly and simmer for 15-20 minutes, until the beetroot and carrots are tender. Allow to cool slightly before puréeing with a stick blender or in batches in a food processor, to form a smooth soup.
While the soup cools, prepare the walnuts: place a non-stick frying over a low-medium heat. Add the sugar, salt and pepper, and when the sugar begins to dissolve, add the walnuts. Tip the pan slightly to allow the dissolving sugar to cover the nuts.
When the sugar mixture has caramelized slightly, tip the mixture out on to an oiled baking sheet. Allow to cool before roughly chopping.
Serve the soup with the candied walnuts and the remaining thyme sprinkled over the top.
*Inspired by Emily J. featured in the Realfood Cookbook