How to Make It
In a medium, heavy saucepan, whisk the eggs with the sugar, tapioca and vanilla bean and seeds until the mixture is pale yellow. Add the half-and-half and bring to a simmer over moderately high heat, whisking constantly. Simmer, whisking, until the mixture is very thick, about 10 minutes. Discard the vanilla bean. Whisk in the vanilla extract.
Pour the pudding into a heatproof dish and let cool for 2 hours before serving. Alternatively, cover the pudding and refrigerate overnight, then serve chilled.