Preheat oven to 350°F. Line a baking sheet with parchment paper, set aside.
Using a stand mixer fitted with a paddle attachment cream the butter, brown sugar, and sugar on medium speed for 1-2 minutes. Add the eggs and vanilla extract and mix until combined.
Add the flour, cocoa, cornstarch, baking soda, and salt. Mix until the dough comes together. Using a ¼ cup measuring spoon portion the dough into round balls. Place the balls on the baking sheet. Using the palm of your hand gently press down on each ball just slightly until it creates a very thick disk. Place 6 per cookie dough balls per baking sheet.
Bake for 10-12 minutes or until edges are set and the center is no longer shiny. Remove from oven and let cool on baking sheet for 5 minutes.
Make Peanut Butter Layer
While the cookies are baking make the peanut butter buckeye layer: cream the butter and peanut butter together. Add the milk, vanilla, and salt and mix to combine. Add the powdered sugar and beat until it comes together. Portion the mixture into 2-3 T sized balls. Press down on each ball with the palm of your hand to create a thick disk.
Final Assembly
Once the cookies have cooled on the baking sheet for 5 minutes, transfer them to a wire rack. Now place a peanut butter buckeye layer on top of each warm cookie.
Melt the milk chocolate chips in the microwave on half power for 60 seconds. Once melted use a spoon to carefully pour some melted chocolate overtop of each peanut butter topped cookie. Let the chocolate set and then enjoy!