Heat half of the milk in a small saucepan with the vanilla (if using a vanilla bean, scrape out the seeds and add them to the milk). Do not boil; just heat until it reaches a simmer, then remove from the heat.
In a bowl, whisk the egg yolks and sugar until light and fluffy. Whisk in the cornstarch and the remaining cold milk. Gradually pour in the warm vanilla milk while whisking constantly.
Pour the entire mixture back into the saucepan and cook over low heat, stirring constantly, until it thickens into a rich cream. Once thickened, remove from the heat and let it cool completely. TIP: For a smoother consistency, strain the finished cream through a fine-mesh sieve.
Place the bao buns in a steamer lined with parchment paper and steam over boiling water for 5-6 minutes, or until softened. Do not open the steamer during steaming to prevent the dough from collapsing.
Carefully open the softened bao buns and fill them with the cooled vanilla cream. Serve immediately or chilled.
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