Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Add the eggs one at a time, mixing well after each addition, then stir in the vanilla extract.
In a separate bowl, whisk together the flour, cocoa powder, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, mixing until just combined. Fold in the chocolate chips.
Using a cookie scoop or tablespoon, drop rounded balls of dough onto the prepared baking sheets, leaving space between each cookie.
Bake for 10-12 minutes, or until the edges are set but the centers are still soft.
Remove from the oven and let cool on the baking sheets for 5 minutes before transferring to wire racks to cool completely.
While the cookies cool, prepare the cookie dough frosting by beating together the softened butter and brown sugar until creamy.
Gradually add the powdered sugar, beating until smooth. Mix in the milk and vanilla extract, then fold in the mini chocolate chips.
Once the cookies are completely cool, spread a generous amount of cookie dough frosting on the bottom of one cookie and top it with another cookie to create a sandwich. Repeat with the remaining cookies.