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Place the caster sugar in a bowl, then rub in the vanilla seeds with your fingers so they’re evenly mixed. Stir in the yogurt until the sugar has dissolved. Churn the mixture in an ice-cream machine until frozen but still soft or, if you don't have a machine, pour the yogurt into a freezer-safe container and freeze for 4-6 hrs, stirring thoroughly every hr or so. Meanwhile, line a 1kg loaf tin with cling film.
Spoon the soft frozen yogurt into the tin, cover with another piece of cling film, then freeze for at least 4 hrs, until firm. Segment the grapefruit, catching the juices in a bowl – you should get about 200ml. Put the juice into a small pan with the honey, simmer for 10-15 mins until thickened and syrupy, stir in the segments, then leave to cool.
Take the yogurt ice from the freezer about 10 mins before you want to serve it. Cut into slices and serve topped with grapefruit, some of the honeyed sauce and a scattering of mint.