Add ¼ cup of the milk, cornstarch, and cocoa powder together in a saucepan. Whisk well until thoroughly combined.
Heat on medium-high and add the remaining milk, brown sugar, salt, and chocolate. Stir frequently until the mixture is steaming hot and the chocolate is completely melted.
Remove the saucepan from heat and stir in the vanilla and bourbon.
Pour the hot chocolate into a mug and top with whipped cream and caramel.
Serve immediately.
Notes
Use cold milk to prevent the cornstarch from getting lumpy.
Add the bourbon and vanilla only when you remove the hot chocolate from the heat.