In a small bowl combine flour, cocoa powder, 2 Tablespoons espresso powder, baking soda and salt. Set aside.
In the bowl of a stand mixer, cream together butter and sugars until light and fluffy. Add egg and vanilla and mix until incorporated. Turn mixer to low and slowly add in the flour mixture.
Add in milk. Refrigerate batter for one hour.
Preheat oven to 350 °F (177 °C). Drop dough in 1 Tablespoon sized drops onto a parchment lined baking sheet. Bake for 11-13 minutes until set. Cool completely.
To make the filling:
Beat together powdered sugar, 1 Tablespoon espresso powder, shortening, and vanilla. Mixture will seem dry at first. Add cold water until mixture becomes spreadable.
To assemble:
Roll 1 teaspoon of filling into a ball. Smoosh between two cookies. Alternatively, if using ice cream, scoop a giant scoop and smoosh between two cookies. Enjoy.