Mix the butter, brown sugar, half-and-half and salt in a saucepan over medium-low heat. Bring the mixture to a simmer and cook, stirring often, until thickened slightly, about 5-7 minutes. Add the vanilla and cook another minute. Remove from heat and allow to cool (or refrigerate for a few minutes).
For the Hot Chocolate
Add milk to a medium saucepan over medium heat. Once warm, stir in the chocolate chips and 1/2 cup of caramel sauce and stir well until chocolate has melted. Serve warm topped with whipped cream or marshmallows and a drizzle of caramel sauce.
Extra caramel sauce can be stored in the refrigerator.