Preheat oven to 350 degrees and lightly grease a 9x13-inch baking pan.
Place chopped chocolate in a small heavy-bottomed saucepan and set over low heat, stirring constantly, until melted. Remove from heat.
Use an electric mixer to cream butter and sugar until fluffy.
Beat in eggs one at a time.
Mix in melted chocolate, adding it gradually if it is still hot.
Mix in vanilla extract and flour. Pour batter into prepared pan.
Sprinkle chocolate chips on top.
Bake for 30 to 35 minutes. Let cool before making frosting.
To make frosting, beat butter until creamy. Gradually beat in confectioners' sugar.
Beat in vanilla and milk until smooth and creamy. Spread on brownies.
Top with desired amount of sprinkles.