In a thick bottom sauce pan warm 2 cups of milk over low heat.
In a bowl cream egg yolks and granulated sugar. Sift in all-purpose flour and cornstarch. Whisk until smooth. Finally stir in vanilla and a pinch of salt.
Pour only ¼ of warm milk into (2) and whisk to combine. Then pour the cream in the pan of the warm milk.
Over medium heat bring it to a boil whisking constantly. When it starts to boil, whisk continually until the cream thickens.
Out of heat stir in ⅓ cup of unsalted butter. Mix until combined. Transfer to a heat-proof bowl and let cool.
Meanwhile cream ⅓ cup of softened butter. When the cream is cooled to room temperature, add in the butter. Whisk until smooth.
Notes
If you want to use a vanilla bean, with a sharp knife, split the bean in half lengthwise. Use the tip of the knife to scrape as many of the seeds as possible from the pod. And add the beans in the milk (1).
Recipe by Eugenie Kitchen at https://eugeniekitchen.com/mousseline-cream/