Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper or a nonstick baking liner and set aside.
In a very large bowl, combine the cake mix and pudding mix. Add in the eggs and shortening (or butter).
Beat until just combined. It may seem crumbly at first, but it will come together.
Using a tablespoon measuring spoon, measure out the dough. Each ball of dough should be exactly 1 tablespoon.
Place the cookie dough balls 2 inches apart on the cookie sheet and bake for 8-10 minutes. You want to slightly under-bake these cookies to keep them soft and fudgy.
In a medium-sized bowl, combine the room temperature butter and brown sugar. Beat until light and creamy.
Add in the salt and vanilla extract. Mix.
Add in the flour and miniature chocolate chips and mix until just combined.
Add in the milk, 1 tablespoon at a time, until desired consistency has been reached. If your frosting is too dry add 1 tablespoon extra milk and if it's too wet, add in some extra flour.
Once the cookies are baked, let them sit on the pan for 3-4 minutes and then transfer to a cooling rack to cool completely.
Once cookies are completely cooled, frost one cookie with the cookie dough frosting and press another cookie on top.