In a medium bowl, whisk together egg yolks, egg, sugar, cornstarch, and salt. Gradually add hot milk mixture to egg mixture, whisking constantly. Return mixture to saucepan; bring to a boil over medium heat, whisking constantly. Continue to cook, whisking constantly, until thickened and mixture no longer tastes starchy, about 3 minutes. Pour through a fine-mesh sieve into a medium bowl, discarding any solids. Stir in butter until melted and combined. Cover with a piece of plastic wrap, pressing wrap directly onto surface of cream to prevent a skin from forming. Refrigerate until thoroughly chilled, about 3 hours, or up to overnight. Stir until smooth before using.