In a medium saucepan, heat milk, 3 tablespoons (36 grams) sugar, vanilla bean paste, and salt over medium-low heat, stirring frequently, just until steaming. (Do not boil.)

In a medium bowl, whisk together egg yolks and remaining 3 tablespoons (36 grams) sugar. Slowly add half of hot milk mixture, whisking constantly. Whisk egg yolk mixture into remaining hot milk mixture in pan. Cook over medium heat, whisking constantly, until mixture is thick enough to coat the back of a spoon and an instant-read thermometer registers 180°F (82°C).

Strain mixture through a fine-mesh sieve into a medium heatproof bowl, discarding solids. Cover with plastic wrap, pressing wrap directly onto surface of mixture to prevent a skin from forming. Refrigerate until cold, at least 4 hours, or up to overnight. Refrigerate in an airtight container for up to 4 days.