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Put the sweet potato into a microwave-proof bowl, add 1 tsp water and cook on High for 2 mins. Mash in a large bowl.
Put the chickpeas and chestnuts into a food processor and pulse until well chopped but not pasty. Tip on top of the sweet potato, then add the egg, spices, garlic and coriander. Season generously and mix well with your hands. Add the cranberries. Shape dessertspoon-sized balls of the mix into 20 or so patties. Can be made ahead and chilled for up to 3 days.
Heat 2 tbsp oil in a large non-stick frying pan. Fry half of the falafels for 2 mins on each side until golden. Lift onto kitchen paper to drain. Repeat with the second batch. Can be made up to 2 days ahead and reheated. Let the falafel cool for a few mins before serving with the yogurt, plus a scattering of coriander.