In a medium sauce pan, pour milk and heavy cream. Heat over medium-high heat. Watch carefully. You do not want it to boil or scald.
In a large bowl, whisk together cocoa, sugar and milk chocolate.
Slowly add this dry mixture to the milk mixture until completely combined.
Reduce heat to medium.
Add in sweetened condensed milk and vanilla, and stir until completely combined.
Reduce heat to low and simmer for 5 minutes.
Remove from heat and serve in individual mugs.
Top with whipped cream, ground cinnamon, and additional chocolate shavings, if desired.
Notes
The original recipe calls for 1 ½ cups cocoa. If you want a creamier, thicker cocoa like the one they serve at the restaurant, you'll want to add more cocoa.