Heat the oil in a large saucepan over a medium heat. Add the onion and a pinch of salt. Cook for 10 minutes, stirring occasionally, until the onion begins to colour. Add the garlic and cumin and cook for 2 more minutes to release their flavour.
Add the beetroot and potato then pour in the water. Bring to a gentle simmer and cook for about 15 minutes until soft. Place the vegetables and their cooking liquid into a blender or food processor and blend until just smooth. You may need to do this in two stages.
Return to the pan and add the vinegar, half the parsley and salt and pepper to taste. Serve with a little yoghurt on top, the rest of the parsley and an extra drizzle of olive oil.