How to Make It
In a large saucepan, combine the tapioca, whole milk, vanilla bean and seeds and a pinch of salt. Bring to a simmer over moderate heat and cook, whisking occasionally, until the tapioca is translucent and tender, about 20 minutes. Whisk in the coconut milk.
In a small bowl, whisk the egg yolks with the sugar. Gradually whisk in half of the warm tapioca in a steady stream. Continue whisking and pour the egg yolk mixture back into the saucepan. Cook the pudding over moderate heat, stirring occasionally, until thickened, about 5 minutes. Transfer the pudding to a bowl and let cool to room temperature. Discard the vanilla bean.
In a medium bowl, combine the mango, lime zest and juice. Transfer half to a food processor and puree until smooth. Stir the puree into the diced mango. Divide half of the fruit into 4 glasses, top with the tapioca pudding, then top with the remaining fruit. Cover the puddings and refrigerate for about 2 hours, or until chilled, before serving.
The assembled puddings can be refrigerated overnight. Let them stand at room temperature for about 30 minutes before serving.