Preheat oven to 350°F (177°C). Grease 2-inch cake pans (or more if you have more than 2), line with parchment paper, then grease the parchment paper. Parchment paper helps the small cookie cakes seamlessly release from the pans.
Add the dry ingredients to the wet ingredients and mix on low until combined. With the mixer running on low speed, stir in the mini chocolate chips. Dough will be thick and sticky.
Divide cookie dough between however many cake pans you're using. Press evenly into each. I only have 2 6-inch cake pans, so I baked in batches. If baking in batches, cover any cookie dough that isn't being used and set aside at room temperature.
Bake for 17 - 20 minutes or until the cake layers are lightly brown on top and a toothpick inserted in the center comes out mostly clean. Allow cakes to cool for 10 minutes in the pans. Run a sharp knife around the edges, then carefully invert the pan so the warm cookie cake slides out. (At this point you can clean out pans, grease, line with parchment, grease parchment, then bake remaining cakes if needed.) Set the baked cakes on a wire rack to cool completely. The cakes must be completely cool before frosting and assembling.
With a handheld or stand mixer fitted with a paddle or whisk attachment, beat the butter and peanut butter together on medium speed until creamy and smooth, about 2 minutes. Add confectioners' sugar, cocoa powder, vanilla extract, and 1 Tablespoon milk. Mix on low speed for 30 seconds, then increase to high speed and beat for 2 minutes. Add another Tablespoon of milk if frosting is too thick. If too thin add more confectioners' sugar.