To make Baileys cream, beat whipping or heavy cream and Baileys in the bowl of stand mixer fitted with the whisk attachment at medium speed until soft peaks form about 4-5 minutes ( Do not over beat so the mixture doesn't curdle). Cover and refrigerate until ready to use.
Place chocolate in a heatproof bowl and sit over a pan of barely simmering water and allow chocolate to melt , stirring occasionally. Set aside once melted
Add milk to a saucepan and stir in melted chocolate. Bring to a low boil, stirring occasionally. Add chocolate liqueur and vanilla extract. Cook for about a minute.
Divide hot chocolate between 2 mugs and top with Baileys cream.