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Drain the syrup from two cans of lychees into a small pan. Add the sugar and dissolve over a gentle heat. Bring to the boil for 1 min.
Blitz the drained lychees in a food processor until very finely chopped. Pour in the lime juice and syrup with the blade still whirring – don’t worry if the mix isn’t perfectly smooth at this point. Tip into a 1-litre container and freeze for at least 6 hrs until solid.
Break up the frozen mix, then return to the bowl of the processor. Tip in the egg white and whizz until thick, pale and smooth. Add zest from 1 lime. Return to the container and freeze again, ideally overnight. Serve in scoops with remaining lychees scattered with a remaining zest.