Peel the potatoes, parsnips, and carrots as desired, then chop them into small pieces.
In a large saucepan, heat the oil over medium-high heat. Add the potatoes, parsnips, carrots, green onions, and ginger. Stir to coat. Add the coconut milk, plus 1 can of water. Stir, then bring to a boil; lower the heat and simmer for about 20 minutes, or until the veggies are tender. Add the nutmeg, salt, and pepper.
Puree the soup in a blender in small batches. Garnish with nutmeg before serving.