Preheat oven to 375°F. In a large mixing bowl beat butter and shortening with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar, brown sugar, baking soda, and salt. Beat until combined, scraping sides of bowl occasionally. Beat in eggs and vanilla until combined. Beat in cocoa powder. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour.Advertisement
Drop dough by rounded teaspoons 2 inches apart onto an ungreased cookie sheet (or use a small to medium cookie scoop to drop dough). Spoon marshmallow creme into a pastry bag fitted with a small round (1/4-inch) tip. Insert the tip into each mound of dough and squeeze some of the marshmallow creme into each mound.
Bake for 8 to 9 minutes or until edges are firm. Cool on cookie sheet for 2 minutes. Transfer cookies to a wire rack; cool.
For icing, in a small saucepan cook and stir chocolate pieces and sweetened condensed milk over low heat until melted and smooth. Stir in the 1 tablespoon milk. If necessary, stir in additional milk, 1/2 teaspoon at a time, to reach glazing consistency. Spread cookies with icing. Let stand until icing is set.
Place cookies in a single layer in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months.