To make the soup, place the oil into a saucepan over a medium heat. Add the garlic and shallot and fry for two minutes, until softened.
Add the sweet potato and fry for two minutes, until beginning to brown.
Add the stock and bring to the boil, then reduce the heat to simmer for 15 minutes, stirring occasionally, until the sweet potato is soft and cooked.
Season, to taste, with salt and freshly ground black pepper and liquidise with a hand-held blender.
To make the coriander pesto, place the herbs and oil in a food processor, season well with salt and freshly ground black pepper and blend to a smooth paste.
To serve, pour the soup into a warm bowl and drizzle with the pesto.