Heat milk and cinnamon to just below simmer (must not boil). Remove from heat, cover and let stand for 15 minutes.
Add the Kahlua to the milk and mix.
Place plastic wrap on top of the milk so that no skin forms and refrigerate for about 4 hours (skip this part for a warm milk shake).
Dip the glass rim into some Khalua and then press against the sugar to coat the rim of the glass
Place a heaped tablespoon of caramel sauce in the bottom of the glass.
Gently pour the cinnamon milk up to ¾ of the glass.
Spoon a scoop of vanilla ice cream on top and sprinkle with some nutmeg and serve.