Preheat oven to 350°.
Heat milk in a saucepan at medium heat until small bubbles form on the sides.
Reduce heat to low and add chocolate, half of the sugar and stir until smooth. Remove from heat and let cool.
In a separate bowl, mix the butter, remaining sugar, and vanilla with an electric mixer.
Add the egg, mixing until well blended.
Pour in cooled chocolate mixture, alternating with flour and mix well. Add chocolate chips.
Spoon batter into muffin tins, lined with paper muffin cups.
Bake at 350° for 15-18 minutes. Let cool then frost with chocolate frosting.