In the top of a double boiler melt the chocolate. In a separate heavy saucepan, heat the milk and cream on low until hot (don't let it bubble). Once hot, add 3 tablespoons of this milk and cream to the melted chocolate and mix well. Blend in the rest of the hot milk/cream mixture, and add sugar and cinnamon.
Combine the eggs and vanilla, and beat together in a bowl. Add a tablespoon of the chocolate mixture to the eggs and beat well. Slowly stir the entire egg mixture into the chocolate mixture. Whisk the hot chocolate briskly in the double boiler for three minutes.
While waiting, pour white chocolate liqueur or creme de cacao in mugs. For a peppermint flavor, add the schnapps. Add hot chocolate mixture. Serve immediately.