Place the milk, sugar and salt in a small sauce pan. Scrape the seeds from the vanilla bean and add the seeds and pod to the milk. Heat over medium high until scalding.

Meanwhile, in a large bowl use a hand whisk to combine the eggs, yolks and cornstarch until smooth.

Whisk the scalding milk into the egg mixture, then return the custard to the pan. Cook over low heat, stirring constantly, until the mixture thickens and just begins to boil.

Immediately strain the pastry cream back into a the bowl. Add the butter and rum. Stir until the butter is melted.

Cover with waxed paper or buttered parchment directly on the surface and cool to room temperature, chill several hours or overnight until completely cooled and set.