Put the sugar and measured water into a saucepan, add the lemon rind and gently heat until the sugar has dissolved. Increase the heat and boil for 2 minutes.
Tear the tips off the mint stems and finely chop to give about 3 tablespoons, then reserve. Add the larger mint leaves and stems to the hot syrup and leave for 1 hour to cool and for the flavours to develop.
Strain the syrup into a jug, add the chopped mint and top up to 600 ml (1 pint) with extra cold water. Pour into a small roasting tin and freeze the mixture for 2–3 hours or until mushy.
Break up the ice crystals with a fork, then return to the freezer for 2–3 more hours, breaking up with a fork once or twice until the mixture is the consistency of crushed ice. Serve now, spooned into small glass tumblers, decorated with tiny sprigs of mint dusted with icing sugar, or leave in the freezer until required. If leaving in the freezer, allow to soften for 15 minutes before serving. If frozen overnight or longer, break up with a fork before serving.