In a heavy soup pot, heat the oil and sauté the onions until soft. Add the carrots, sliced ginger and stock. Bring to a simmer and cook until tender.
Stir in the coconut milk. In the bowl of your blender or food processor, puree in small batches until smooth. Return to the pot and season to taste with sea salt and fresh pepper.
To serve, ladle into soup plates. Top each bowl with a dollop of Greek yogurt and sprinkle with chopped, fresh chives.