If you wish, soak the tapioca pearls in cold water for 15 to 20 minutes, then drain them.
Pour the milk into a medium saucepan, then add the sugar, cinnamon stick and lemon zest.
Heat over a medium heat, stirring occasionally, until the milk is just below boiling point and not yet bubbling.
Stir in the drained tapioca pearls, reduce the heat to medium–low and cook, stirring constantly, for 15 to 20 minutes, until the pearls turn translucent and the mixture thickens.
Remove the pan from the heat, discard the cinnamon stick and lemon zest, then stir in the vanilla extract.
Serve warm or chilled. To serve chilled, divide between individual bowls, leave to cool at room temperature, then chill in the fridge for at least 2 hours.
Store any leftovers in an airtight container in the fridge for up to 3 days.