Heat the sugar, measurement water and lemon rind in a saucepan over a gentle heat until the sugar is dissolved. Increase the heat and boil for 2 minutes, then remove the pan from the heat.
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 through a sieve into a jug, add the chopped mint and top up to 600 ml (1 pint) with the lemon juice and 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 a further 2–3 hours, breaking up with a fork once or twice more until the mixture is the consistency of crushed ice.
Spoon into glass tumblers and decorate with tiny mint sprigs dusted with icing sugar before serving, 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.