In a large stockpot or Dutch oven, heat the butter, ghee or oil. Over medium-high heat, sauté the parsnips until lightly browned, about 10 minutes. Add the potatoes and vinegar and scrape up any brown bits that formed on the bottom of the pan.
Pour in the coconut milk, vegetable stock and salt. Bring to a boil, cover and reduce the heat to medium-low. Simmer the parsnips and potatoes until fork-tender, about 15 more minutes.
Meanwhile, make the oil: in a small saucepan, gently heat the garlic, chili flakes and olive oil over a medium-low flame until very fragrant, about 10 minutes. If the garlic begins to brown, reduce the heat. Allow to cool to room temperature, then strain the garlic and chili through a fine mesh strainer and store in an airtight glass jar for up to a week.
When the soup is ready, remove from the heat and stir in the parsley, basil and chives. Transfer the soup immediately to a blender (or use an immersion blender) and puree until smooth, adding more stock as necessary to reach your desired consistency.
Ladle the soup into bowls and garnish with excess herbs and the chili-garlic oil.