Heat the milk in a small saucepan over medium heat until it begins to simmer. Do not boil.
Whisk in the cocoa powder and sugar until dissolved.
Add the chocolate chips and stir until completely melted and smooth.
Remove from heat and stir in the Kahlua.
Pour into mugs, top with whipped cream and chocolate shavings.
Notes
For an extra indulgent version, add a splash of Baileys Irish Cream along with the Kahlua. Use dark chocolate chips for a richer, more intense chocolate flavor.