In a large mixing bowl, whisk the yogurt, sugar and matcha powder well until the sugar is dissolved. Cover and chill for 1 hr or until the mixture is very cold. Pour into an ice-cream machine following the manufacturer's instructions. Scrape into a freezable container and freeze for 4-5 hrs until firm.
To make the sesame brittle, line a baking sheet with baking parchment. Heat the sugar in a medium saucepan. Leave to melt, without stirring, for about 5 mins until bubbling and golden. Stir the sesame seeds into the light caramel, boil for a few secs, then pour the mix onto the baking sheet, spreading as thin as possible. Once hardened, bash the brittle on the counter to crack into pieces. Can be made 1 week in advance and stored in an airtight tin.
Remove the frozen yogurt from the freezer 1 hr or so before serving, to soften slightly. Spoon into small bowls with the sesame brittle scattered over.