Whisk together the milk, heavy cream, sugar, vanilla extract, and peppermint extract until the sugar is dissolved. Churn according to ice cream maker's manufacturer's instructions. Add the dark chocolate chunks in when indicated by your ice cream maker's manufacturer. If no instructions are included on when to mix them in, stir them in at the end of the churning. Eat immediately for soft serve consistency or pack into a freezer safe container. Lay plastic wrap directly on the surface of the ice cream and freeze for at least two hours or until firm.