Peel the carrots and sweet potatoes, and cut them into pieces (the smaller they are, the faster they'll cook).
In a pot, sauté the cubed carrots and sweet potatoes in oil until they are fragrant (but not browned).
Add water, coconut milk, curry powder and grated ginger, and cook on medium heat until the carrots and sweet potatoes are soft (10-20 minutes, depending on the size you cut them).
Puree the soup with an immersion blender, and add salt and pepper to your liking.
Divide the soup among bowls and serve topped with sunflower seeds and cilantro leaves.