Preheat the oven to 350F. Line a 6 cup standard muffin pan with paper liners. In a medium bowl, whisk together the flour and sugar, then add the chocolate chips. In a small mixing bowl, combine the egg, milk, melted butter, and vanilla. Add the flour mixture and stir until just moistened.
Divide the mix among the prepared muffin cups. Bake until the tops spring back when lightly tapped, 20-25 minutes. Remove from the oven and cool in the pan for 10 minutes, then transfer to a wire rack to cool.
For the frosting, put the chocolate, cream and butter in a heatproof bowl over but not touching a pan of simmering water. Stir gently over low heat until smooth. Chill until firm but spreadable, then pipe or spread over the cooled cupcakes.