In a mixing bowl, cream butter and sugar. Beat in the egg, egg yolks, orange peel and extract. Combine the flour, ginger and baking soda; gradually add to creamed mixture.
Drop by rounded tablespoonfuls 2 in. apart onto ungreased baking sheets. Bake at 300 degrees F for 21-23 minutes or until golden brown. Remove to wire racks to cool.
In a saucepan, combine the marshmallow creme, sugar, milk, butter, and salt. Bring to a rolling boil over medium heat; boil for 5 minutes, stirring constantly. Remove from the heat. Add chocolate chips and vanilla; stir until chips are melted. Spread over tops of cookies.