In a medium saucepan, heat milk over medium heat until steaming. (Do not boil.)

In a medium bowl, whisk together sugar, cornstarch, and salt. Whisk in egg yolks until well combined. (Mixture will be very thick.) Gradually add hot milk, whisking constantly. Pour egg mixture into saucepan. Bring to a boil over medium heat, whisking constantly. Cook, whisking constantly, until thickened and bubbly and an instant- read thermometer registers 185°F (85°C), 3 to 4 minutes. Remove from heat. Stir in butter until melted and smooth.

Pour and press mixture through a fine-mesh sieve into a heatproof bowl, discarding solids; stir in Vanilla Bean Paste. Cover with plastic wrap, pressing wrap directly onto surface of custard to prevent a skin from forming. Refrigerate until thick and cold, at least 2 to 3 hours, or overnight. Stir cold custard until softened and smooth before using.