Heat 1 quart whole milk in a medium saucepan over medium heat just until simmering. Whisk in 4 ounces chopped unsweetened chocolate, ½ cup semi-sweet chocolate chips, ¼ cup packed light brown sugar, and 1 pinch kosher salt until the chocolate is melted and the hot chocolate comes to a simmer (do not let it boil). Reduce the heat to low and simmer for 5 minutes.
Turn off the heat. Whisk in ½ teaspoon vanilla extract. Pour into mugs and serve with marshmallows and whipped cream if desired.
