Make the Vanilla Cream
In a medium bowl, whisk the egg yolks until smooth. In a medium saucepan, combine the milk, cream, sugar, cornstarch and vanilla bean paste and whisk until smooth. Cook over moderate heat, whisking constantly, until the mixture comes to a gentle simmer and thickens, about 5 minutes. While whisking constantly, drizzle one-third of the milk mixture into the egg yolks. Slowly drizzle the egg yolk mixture back into the saucepan, whisking constantly. Cook over moderately low heat, stirring occasionally, until the mixture is very thick, 2 to 3 minutes. Whisk in the butter, then strain the custard into a medium heatproof bowl. Press a piece of plastic wrap onto the surface of the vanilla cream and refrigerate until cold, about 2 hours.