In a medium saucepan, whisk together the milk, cream, brown sugar, and egg yolks until fully combined.
Place the saucepan over medium-low heat and cook, stirring constantly with a rubber spatula or wooden spoon, until the mixture thickens slightly and reaches 175 to 180°F. Do not let it boil.
Remove from heat. Pour the custard through a fine mesh sieve into a clean bowl. Stir in the vanilla and salt.
Cover and refrigerate for at least 4 hours or overnight, until thoroughly chilled. Churn when cold.