Pour the milk and vanilla into the slow cooker; whisk in cocoa powder and cover.
Cook on HIGH for 2 hours.
Remove lid and stir in chopped chocolate; stir until melted.
Taste for sweetness and decide if you want to add some sugar to the mixture. If you decide to add sugar, whisk in a tablespoon of sugar at a time. Taste and adjust accordingly.
Prepare a cornstarch slurry by combining milk and cornstarch in a small mixing bowl; mix until smooth paste forms.
Whisk the cornstarch slurry into the hot chocolate mixture; whisk until well combined.
Cover with a lid and continue to cook for 1 more hour, or until thickened. I suggest to whisk occasionally so to prevent any lumps.
When ready, remove the lid and ladle the hot chocolate into mugs.
Garnish with whipped cream and chocolate shavings.