The secret to making this soup really smooth is to let the blender do a good job. Sometimes I blend the soup, strain it to remove any fibrous sweet-potato pieces, then give it a second spin to make it silky. I also strongly recommend that, for the best flavour, you use fresh-ground natural peanut butter with no added sugar.
In a medium pot, combine olive oil, onion, carrot and celery. Cook gently over medium heat until vegetables are soft and translucent.
Add sweet potatoes, coconut milk and water. Bring to a boil and then turn down; let the soup simmer until sweet potatoes are soft (approximately 10 minutes; test them by piercing with a fork). At this point the soup is ready to purée.
Pour into a blender,then add peanut butter, cayenne pepper and lime juice, and purée until smooth. If necessary to reach the desired consistency, add a little water and whirl in the blender again. Season with salt and pepper to taste.