Preheat the oven to 350°F.
In the bowl of a stand mixer, cream together peanut butter and butter. Add both sugars, and cream together until smooth. Scrape down the bowl, and add egg and vanilla extract.
In a small bowl, stir together flour, arrowroot, salt, baking powder, and baking soda. Add to the peanut butter mixture, and turn on mixer to low speed. Cream together until just combined, scraping down the bowl to ensure all ingredients are well mixed.
Using a 1 ½ tablespoon-sized scoop, scoop the cookie dough onto a parchment lined baking sheet, about 2 inches apart. Using the tines of a fork, gently press the cookies down in a criss cross pattern.
Place in the oven and bake for 8-10 minutes, spinning halfway through. Remove cookies from the oven and place on a cooling rack to cool completely before sandwiching with the icing.
To make the icing, place butter and cream cheese in the bowl of a stand mixer fitted with a paddle attachment. On medium speed, cream together butter and cream cheese until well combined, and no cream cheese lumps are present. Scrape down the bowl and add the powdered sugar, vanilla, and salt. Turning the mixer on low, combine the ingredients until the powdered sugar is mixed in. Turn the mixer up to medium-high speed, and cream together until light and fluffy.
Meanwhile, place the chocolate in a small microwave safe bowl, and place in the microwave for 1 minute. Stir together, and if needed, microwave for 20 seconds at a time, until the chocolate is melted. Add the chocolate to the cream cheese mixture, and mix until well combined, scraping down the bowl as needed.
Once cookies are baked and cooled, place the cream cheese frosting in a piping bag fitted with a small piping tip. (NOTE: You can use any shape desired.) Pipe about 1-1 ½ tablespoons of frosting onto one cookie, and sandwich with another cookie. Refrigerate for 15 minutes to all the icing to harden slightly. ENJOY!