Preheat oven to 350F/175C and line cookie sheets with parchment paper.
In large, microwave-safe bowl, combine butter and chocolate chips. Microwave for 30 seconds and stir, repeating at 15 second increments until chocolate and butter are completely melted.
Remove from microwave, stir well, and allow to cool slightly before proceeding.
Once butter/chocolate mixture has cooled, stir in sugars, eggs and vanilla.
In separate, medium-sized bowl, whisk together flour, cocoa powder, cornstarch, baking powder, baking soda, and salt.
Gradually stir flour mixture into butter mixture until completely combined.
Drop cookie dough by rounded 2 teaspoon-sized scoop onto parchment paper, pressing down slightly. Bake in 350F/175C oven for 8-10 minutes, then allow to cool on cookie sheet.
Filling: In KitchenAid or with electric handmixer, cream together peanut butter and butter.
With mixer on low-speed, gradually stir in powdered sugar until completely combined (be sure to scrape down the sides of the bowl so all ingredients are well incorporated).
Stir in vanilla extract.
Add milk, one Tablespoon at a time, until well-combined. Check the consistency at 3 Tbsp and if it is much too thick add the fourth Tablespoon (conversely, if you make it too runny, you may add more powdered sugar).
Spread or pipe (I used an Ateco 848 piping tip) the filling onto the bottom of one of your cooled cookies. Sandwich with another evenly-sized cookie.
Once all cookies have been filled and paired, melt chocolate according to package instructions and dip cookies ⅓-½ of the way in your melted chocolate. Immediately sprinkle with chocolate jimmies, if desired, and allow to harden before enjoying.