In a medium bowl, whisk together the egg yolks and sugar until well combined. Sift the flour and cornstarch into the bowl with the eggs, whisking until smooth.
Add the milk to a medium saucepan. Scrape the vanilla bean seeds into the milk then add the scraped bean to the saucepan and bring the mixture to a boil just until the milk starts to foam. Remove the milk mixture from the heat, take out the vanilla bean and then very slowly whisk the milk into the egg mixture, whisking constantly to prevent curdling.
Pour the mixture into a medium saucepan set over medium heat. Cook it, whisking constantly, until it comes to a boil. Once it boils, continue whisking constantly for an additional 30 to 60 seconds until it thickens. Immediately pour the mixture into a clean bowl and cover it with plastic wrap so that the plastic wrap is touching the pastry cream. Place the bowl inside a larger bowl filled with ice water to bring it to room temperature.
Once the pastry cream is at room temp, whisk it to remove any lumps then pour it into the completely cooled tart shell. Arrange the mango slices on top, starting in the center and then fanning them outwards to mimic flower petals. Slice and serve the tart immediately or store it, covered in plastic wrap, in the fridge for a maximum of two hours before serving.