Brew the coffee in a Moka or espresso machine.
If you are topping your drink with whipped cream, beat the heavy whipping cream in a stainless steel or glass bowl on high speed until the cream is the consistency you desire (stiff peaks vs. thick and creamy, etc.). Set aside.
Add the white chocolate and milk to a small saucepan and turn the heat on medium-low. Mix together until the chocolate is melted.
Turn the heat off, and use a milk frother to froth the milk.
Add the coffee to your mug. Pour the frothed milk into the coffee. Top with the whipped cream and dust with white chocolate shavings and crushed peppermints.