To make the basic hot chocolate, combine the milk with the half-and-half in a small saucepan. Warm over medium-low heat, and then stir in the chocolate chips. Stir until melted (though there will still be lovely particles of chocolate throughout). If it's too chocolaty for you, splash in a little more milk. Add a splash of vanilla extract. If it's not quite sweet enough for you, add 1 teaspoon or so of sugar. Serve in mugs with whipped cream.