Make the Tapioca: Place the milk, coconut milk, and sugar in a heavy bottom pot, like a small dutch oven and bring to a simmer over medium heat (Use a big enough pot as milk tends to boil over very quickly). Pour in the tapioca slowly, while whisking the milk. (If the liquid is not simmering, the tapioca will stick together and you will create one goey raft of tapioca). 

Lower heat to medium low and cook, stirring regularly with a wooden spoon or whisk, until the tapioca is thickened and the pearls are translucent, about 40-45 minutes. 

Turn the heat off and add the vanilla extract, stirring to combine. Then let the tapioca sit for another 5 minutes. 

Chill tapioca: Pour the tapioca into 6 small bowls, using a spatula to scrape the last bit out of the pan. Cover and refrigerate for several hours until cold.

Serve tapioca: Peel the mango with a sharp knife. Cut the two meaty halves off and slice the mango into thin pieces. Fan the mango over the tapioca and serve immediately.