In a stand mixer fitted with the paddle attachment, add the butter and brown sugar and beat on medium-high speed until light and fluffy, about 2 minutes.
Use a silicone spatula to scrape down the sides and bottom of the bowl, then add in the egg and vanilla. Beat on medium-high until mixture is fluffy and pale in color, about 2 minutes.
Stop the mixer and scrape down the bowl, then add the flour, cocoa powder, baking soda, and salt and beat on low speed until just combined and no streaks of flour remain.
Use a 2 ounce cookie scoop to portion out equal amounts of dough. Place on the prepared baking sheets, spacing the dough 2 inches apart. Bake until the cookies have puffed up and are set and firm around the edges but still somewhat soft in the middle, 11 to 12 minutes. As soon as they come out of the oven take the cookie scoop and press the round side of it into the cookies, making an indentation in the center of each cookie. This will create a little cradle for you to put the peanut butter filling in! Transfer the cookies to a cooling rack to cool completely.
Once the cookies have cooled, make the peanut butter filling. Combine the peanut butter, powdered sugar and vanilla in a medium bowl and mix to combine. The mixture will be thick! Scoop out about 1 1/2 tablespoons of peanut butter onto each cookie, gently patting it into rounded disc into the indentation.
Next make the chocolate topping. Place the cream in a medium microwave-safe bowl. Microwave until the cream is hot to the touch but not boiling, 30 to 45 seconds depending on the strength of your microwave. Add the chocolate chips to the cream and let sit for 1 minute, then use a fork to stir the mixture together until smooth and glossy.
Use a small offset spatula or a spoon to top each cookie with about a tablespoon of ganache, spreading it in evenly over the peanut butter filling. Let the ganache set completely, about 30 minutes before serving! Enjoy!