In a medium saucepan, combine milk, half of the sugar, vanilla bean, and salt. Cook over medium heat until mixture comes to a simmer.
In a medium bowl, whisk together egg yolks, remaining sugar, and vanilla bean seeds. Whisk until sugar has dissolved slightly. Whisk in the cornstarch until well combined.
Whisking constantly, slowly pour about 1/2 cup of the hot-milk mixture into the egg-yolk mixture, 1/2 cup at a time, until it has been incorporated.
Pour mixture back into saucepan, and cook over medium heat, whisking constantly, until it thickens and registers a temperature of 175 °F
Remove and discard vanilla bean. Transfer to a mixing bowl. Add the butter, and whisk well until the butter melts and the mixture cools, about 5 minutes. Cover with plastic wrap, pressing it directly onto the surface of the pastry cream to prevent a skin from forming. Refrigerate until chilled.
Caramelized Sugar
Place three cups of sugar into a cold sauce pan over medium heat. Allow the heat to caramelize the sugar and do not start stirring until 1/4 of the sugar is dissolved. Heat the sugar between 295°F-309°F (hard crack stage)
Assembly
Place the pastry cream into a disposable piping fitted with a small round or small star tip. Flip the croissant onto the back fill it with the pastry cream in three spots (the two ends and middle).
Dip the top of the croissant into the caramelized sugar and place on a piece of parchment paper to set about 3 minutes.
Optional you may torch the caramelized sugar to have burnt flavor like that of creme brûlée