Whisk egg in a small bowl and set aside.
 
Combine milk, cocoa, sugar, and corn starch in a medium-sized saucepan.  Blend well, then heat on medium low while stirring constantly until thick, about 5-7 minutes.
 
Remove from the heat and pour one ladle of the mixture into the egg bowl and whisk quickly.  Pour the egg mixture into the cocoa mixture and return to heat and cook until it just boiling.
 
Turn off the heat and add the chocolate and butter.  Stir and make sure both are melted and mixed together well.  Then stir in the Irish Cream.
 
Pour into 3-4 small bowls.  Chill for a couple hours before serving.  Top with whipped cream and sprinkle with shaved dark chocolate or cocoa powder.