For the lamb, preheat the oven to 220C/425F/Gas 7.
Season the lamb loin all ove with salt and freshly ground black peppe, to taste
Heat the butter and oil in an ovenproof frying pan over a medium heat. Add the seasoned lamb and fry for 6-8 minutes, turning regularly, until browned on all sides.
Add the star anise and thyme, then transfer the pan to the oven and cook for 7-8 minutes (for medium), or until cooked to your liking. Remove from the oven and set the lamb aside on a warm plate to rest for 10 minutes. Reserve the pan juices in the pan.
Meanwhile, add the chicken stock to the pan the lamb was cooked in and bring to a simmer, scraping up any browned bits from the bottom of the pan using a wooden spoon, to deglaze. Continue to simmer until the volume of liquid has reduced by half and the pan juices have thickened. Season, to taste, with salt and freshly ground black pepper. Set aside and keep warm.
For the sautéed sweet potatoes, heat the butter and olive oil in a frying pan over a medium heat. When the butter is foaming, add the onion and fry for 1-2 minutes, or until just softened.
Add the star anise, thyme and cubed sweet potato and fry, stirring regularly, for 4-5 minutes, or until the sweet potato cubes are tender and golden-brown. Remove the star anise and discard (or rinse and save for another recipe).
For the sweet potato crisps, heat the oil in a deep fat fryer to 190C. Alternatively, half-fill a deep heavy-based frying pan with oil and heat until a breadcrumb sizzles and turns brown in 30 seconds when when dropped into it. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Carefully lower the potato slices into the hot oil and fry for 30-45 seconds, or until crisp and golden-brown. Remove from the pan using a slotted spoon and set aside to drain on kitchen paper, then season, to taste, with salt and freshly ground black pepper.
To serve, place a medium sized chefs' ring into the centre of each of four serving plates. Fill each with some of the sautéed sweet potato, pressing down using the back of a spoon to compress. Carefully remove the chefs' rings. Carve the lamb loin into thick slices and arrange a few slices on top of each sweet potato tower. Sprinkle over the amaranth and coriander leaves and place one sweet potato crisp on top of each. Drizzle the reduced pan juices around the edge of the plate.