In a medium microwave safe bowl, place the butter and chocolate chips in microwave, stirring every 30 seconds until melted. Whisk in the sugar until well combined. Whisk in the vanilla and chocolate. Whisk in the egg until combined.
In another bowl, whisk flour, cocoa, salt and soda until combined. Stir flour mixture into the chocolate mixture. Beat with a mixer until the dough comes together as a solid.
Transfer the dough to a sheet of wax paper. Shape into a log about 2 1/2 inches in diameter. Place log along the edge of wax paper and roll. Shape as you roll to maintain a smooth cylinder. Twist ends of paper to secure and help keep the shape compact. Refrigerate at least two hours or until firm. If log settles and flattens on one side, rotate every 15 minutes or so to maintain a round shape.
Heat oven to 325 degrees and line baking sheet with parchment paper.
Cut dough in quarter inch thick slices and place on prepared baking sheet. Bake for about 12-18 minutes or until cookies are firm to the touch. Just watch them because it’s hard to tell by looks if they are done since they are so dark to begin with. These baked in batches well, so bake a few to test if you have time. And if your cookies are smaller, adjust the baking time.
Cool and prepare the filling. In a mixer, beat the butter until smooth and creamy. Add sugar and vanilla and beat until smooth. Add milk and salt and continue beating until smooth again. Place about tablespoon of filling on the bottom of one cookie and about a tablespoon of peanut butter on another cookie. Sandwich the cookies together. Repeat with remaining cookies.