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Put the lime wedges in a large jug with the sugar, then use a muddler or the end of a rolling pin to break them down. Release as much juice from the wedges as possible, and let it mix with the sugar to create a syrup – you can also do this with a large pestle and mortar. Discard the lime peel.
Divide the syrup and cachaça between four glasses, then top with the crushed ice. Serve garnished with lime wedges, if you like.