In a medium sauce pan over medium low heat, combine the white chocolate chips and the heavy cream, stirring consistently until the chocolate has completely melted.
Whisk in the cinnamon. Then whisk in the brown sugar a little bit at a time, stirring consistently to make sure the sugar doesn't just melt to the bottom of the pan. Then whisk in the vanilla (it will bubble up a little).
Add the milk, stirring it in. Bring to a slow simmer, and keep there over low heat for five minutes, stirring regularly.
Serve warm topped with whipped cream and more cinnamon.