In a medium saucepan, lightly beat egg. Add coconut milk, milk, sugar, and tapioca; whisk to combine. Set aside, at least 5 minutes, until tapioca is slightly softened.
Stirring constantly, bring mixture to a boil over medium heat; stir in vanilla. Transfer mixture to a bowl; cover with plastic wrap. Let cool until no longer hot, about 30 minutes. Refrigerate until cold, 2 to 3 hours (or up to 3 days).
Meanwhile, preheat oven to 350 degrees. Spread coconut in a single layer on a rimmed baking sheet. Toast, tossing once or twice, until golden, 10 to 15 minutes; let cool.
Just before serving, whisk pudding to loosen. Divide among four serving glasses or dishes; top with pineapple and toasted coconut.