Heat the oil in a large pot over medium heat. Add the onion, carrots, salt, and several grinds of pepper and sauté until soft, 5 to 8 minutes. Add the garlic and cook for another minute.
Add the sweet potatoes, ginger, lemon juice, 3 cups of the broth, and the coconut milk. Bring to a boil, cover, and reduce the heat to a simmer. Cook until the potatoes are tender, 20 to 30 minutes.
Using a stick blender, puree the soup until very smooth. Or, carefully transfer the hot soup to a blender and blender until smooth. Serve with lemon slices or wedges.
Notes
Use an immersion blender. I love leaving the soup in the pot and using an immersion blender to puree it. This also avoids having to pour boiling hot soup into a blender and back into the pot!. If you don't have an immersion blender, though, no worries, a blender or food processor will be perfect.
Substitute lime juice. I love the tartness of lemon in this soup! Another lovely flavor pairing with sweet potato is lime, so try fresh lime juice instead of lemon if you wish.
Add olive oil and cracked black pepper. A little drizzle of olive oil and a grind of fresh black pepper across each soup bowl just before serving is a special touch.
Add sour cream or yogurt. For a pretty flavor contrast swirl a little sour cream, Greek yogurt, or regular plain yogurt into each serving of soup. Use dairy-free sour cream or yogurt if needed.