Preheat your oven to 350°F (175°C).
In a large bowl, cream the softened butter, granulated sugar, and brown sugar together until light and fluffy.
Add the eggs and vanilla extract to the creamed mixture, mixing until well combined.
In a separate bowl, mix together the flour, cocoa powder, baking powder, and salt.
Gradually fold the dry mixture into the wet mixture until just combined, then fold in the mini chocolate chips.
Drop tablespoon-sized balls of dough onto a lined baking sheet, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are set but the centers are still soft.
Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
Prepare the cookie dough frosting by creaming softened butter with brown sugar until smooth.
Add the flour, milk, and mini chocolate chips to the frosting mixture and mix until combined.
Spread a generous layer of cookie dough frosting on the flat side of one brownie cookie, then top with another cookie to create a sandwich.
Repeat with the remaining cookies and frosting, then serve immediately or store in an airtight container.