Heat the milk, butter, and brown sugar in a saucepan until it begins to steam.

Remove from heat and add the chocolate, vanilla, and salt, stirring gently until the chocolate is melted and the sauce is smooth.

Serve the sauce warm with ice cream, or cool it to room temperature and store it in the refrigerator for 1 to 2 weeks. Rewarm the sauce by putting the jar in a pan of very hot water.