Combine the parmesan, milk and 100 ml (3½ fl oz) water in a saucepan over low–medium heat, stirring until the parmesan is melted. Reduce the heat to low and whisk in the beaten egg. Cook, stirring, until the mixture thickens and reaches 85°C (185°F), about 10 minutes. The mixture will separate and appear curdled. Cool to room temperature, then refrigerate for 1 hour or until chilled.
Place the mixture in an upright blender or food processor and blend until smooth. Transfer to a piping bag fitted with a 1.5 cm (⅝ inch) plain nozzle and refrigerate to firm up slightly before serving.