Combine the milk, coconut milk and vanilla bean and seeds in a medium nonreactive saucepan; bring to a simmer over low heat.
Whisk the egg yolks, sugar and cornstarch together in a large bowl. Slowly whisk the warm milk into the egg mixture. Return the mixture to the pan, set it over medium heat and bring to a boil. Cook, whisking constantly, until thickened. Scrape the mixture into a bowl, remove the vanilla bean and whisk in the rum and vanilla extract. Let the custard cool to room temperature, then cover with plastic wrap and refrigerate until cold, at least 2 hours.