In a large saucepan or soup pot, heat the oil over medium heat and add the onions. Cook, stirring occasionally, for 5 minutes, or until the onions look translucent. Add the parsnips, beets, and water and bring to a boil over medium-high heat. Skim off any dirty foam.
Add the dill, salt, and white pepper, and reduce heat to low; simmer for 30-40 minutes, or until the vegetables are soft.
Add the apple cider vinegar (optional) and puree the mixture for a full 5 minutes using an immersion blender, or puree in batches in a food processor. Add more salt and white pepper to taste.
Serve the soup hot with a dollop of creamy coconut milk or Greek yogurt or sour cream and a sprig of dill, or cold with sliced pickles, if desired (I used both for funsies).
Make ahead: can be made 3 days in advance, or frozen.