Strain the mixture back into the cleaned-out pan and cook over a gentle heat, stirring constantly, until the mixture has thickened and lightly coats the back of a wooden spoon. Do not let the mixture boil or it will curdle. Pour back into the bowl and leave to cool, then cover and chill overnight. The next day, churn in an ice-cream maker, stirring the stem ginger and syrup into the mixture just before freezing. If you do not have an ice cream machine, you can pour the mixture into a shallow container, cover and freeze until firm but not rock hard, then whizz in a food processor until smooth. Re-freeze and repeat the process 2-3 times more. Store in the freezer until needed.