Preheat oven to 350 degrees F (175 degrees C). Line baking sheets with parchment paper.

To make cookies, beat vegetable shortening with sugar in a large mixing bowl using an electric mixer until creamy. Add eggs and vanilla extract and mix. Whisk flour, cocoa powder, and baking soda together, then alternate adding flour mixture and milk to the large bowl until smooth.

Drop dough by tablespoon onto prepared baking sheets, about 2 inches apart, shaping as evenly round as possible.

Bake in preheated oven for 15-20 minutes, watching to avoid burning.

Cool cookies on baking sheets before transferring to wire racks to fully cool.

To make filling, whisk together milk and flour in a saucepan over low heat until smooth and pudding-like. Chill in refrigerator for 30 minutes.

Combine vegetable shortening, butter, sugar, and vanilla in a bowl and mix until fluffy. Beat the chilled milk mixture into the bowl with butter mix until smooth.