In a medium saucepan, combine milk, sugar, cocoa powder, and chocolate. Heat over medium heat and cook, stirring occasionally, until all the sugar dissolves and the chocolate is melted. Remove from heat. Add vanilla, Irish cream liqueur, and Irish whisky. Stir.
Prepare the whip cream. In a large bowl, beat the cream until it starts to form soft peaks, slowly add sugar and vanilla, and continue beating until medium peaks. Do not over beat.
Pour hot chocolate mixture into cups and top with whipped cream. Garnish with chocolate shavings. Serve immediately.