In a cheesecloth-lined large sieve or colander set over a bowl drain yogurt, covered and chilled, 12 hours. Discard liquid in bowl.
With a knife halve vanilla bean lengthwise and scrape out seeds. In a blender purée vanilla seeds, half of drained yogurt, and remaining ingredients. In a bowl stir together vanilla mixture and remaining yogurt.
Transfer mixture to ice-cream maker and freeze.
Transfer frozen yogurt to an airtight container and put in freezer to harden. Frozen yogurt may be made 1 week ahead.
