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Peel the sweet potatoes and cut crossways into slices 2.5cm thick. Lay each potato on a large sheet of foil, keeping the slices together.
Drizzle each potato with the olive oil, sprinkle with the thyme leaves, about half of the chopped chilli and season with plenty of salt and pepper. With your hands, massage the flavourings into each slice. Replace the slices in their original positions. Lay a thyme sprig across the top of each potato and sprinkle with the remaining chilli. Wrap the foil securely round the potatoes to make two parcels. (You can prepare to this stage up to 24 hours ahead.)
Put the foil parcels on the rack over the hottest part of the barbecue and cook for 45 minutes until the potatoes are buttery and softened. (Unwrap and test with the point of a knife to check if they’re ready).