Preheat oven to 350 F. Line baking sheets with parchment paper.
To make cookies, cream together shortening and sugar in a large mixing bowl with an electric mixer. Add eggs and vanilla extract and mix to combine.
In a medium bowl, whisk together flour, cocoa powder, and baking soda. Add flour and milk in several additions to the sugar mixture, alternating between dry ingredients and milk. Mix until smooth.
Drop by tablespoon onto the prepared baking sheets, about 2 inches apart. Bake 15 to 20 minutes in preheated oven, or until the cookies are set in the middle. Remove from oven and allow the cookies to cool for 3 minutes on baking sheets before removing to cooling racks. Let cool completely before assembling cookies.
To make the filling, pour milk into a large saucepan over low heat. Whisk in flour until smooth. Allow the mixture to come to a simmer, whisking constantly. Simmer until mixture has thickened, about 3 minutes. Remove from heat and let cool to room temperature, then refrigerate approximately 30 minutes, until chilled through.
In a large mixing bowl, mix together shortening and butter until combined. Add sugar and vanilla and mix until thoroughly combined. Stir in chilled milk mixture into the butter until smooth and fluffy, 1 to 2 minutes.
To assemble, choose 2 cookies of the same size, and spread a layer of filling on the flat side of one cookie and top with remaining cookie to create the sandwich. Repeat with remaining cookies and frosting. Makes approximately 2 dozen pies.