Add the sugar, cocoa powder and cornstarch to a medium saucepan. Pour in the milk and whisk to combine.
Heat over medium low heat until the pudding thickens and comes to a low boil, whisking almost constantly. When thickened, stir in the butter and continue to stir for another minute or two.
Remove from the heat and stir in the vanilla extract, chopped chocolate, Baileys and salt. Stir really well until the chocolate is completely melted and the Irish Cream and vanilla are incorporated. Set aside to cool. Place in the fridge for 4 hours minimum to thicken.
Pour into 4 individual dishes. Top with whipped cream and chocolate shavings.