Preheat oven to 350°F. Line two cookie sheets with parchment paper or silicone baking mats.
In a medium bowl, whisk together cocoa powder, baking soda, salt, and flour. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream butter and both sugars. Mix in egg and vanilla and mix until smooth. Add dry ingredients and mix until combined.
Scoop 2 tablespoon sized balls of dough onto the cookie sheets. You will get about 15-17 cookies. (Alternately, you can use 1 tablespoon sized balls of dough and get twice as many cookies. Baking time will be less.)
Bake for 8-9 minutes until they just lose their glossy sheen. Err on the side of underdone for these cookies; they taste better that way. Let cool completely before filling and making sandwiches.
To make the filling: beat butter and peanut butter in the bowl of a stand mixer fitted with the paddle attachment. Mix in salt, then slowly beat in powdered sugar. Add vanilla, then 2 tablespoons of cream. Add a third tablespoon of cream as needed for the consistency you want. Note: this makes a lot of frosting, more than you need. It is enough frosting to fill the 2 tablespoon sized cookies OR the 1 tablespoon sized, plus extra. Filling can be frozen in an airtight container for up to one month.
Once cookies are cooled, frost half with the frosting and sandwich with the other half. The best way to do this is to place your frosting in a gallon size ziploc bag and cut off one tip. Place a very large squeeze of frosting in the center of the bottom of a cookie, then press the top cookie on top, causing the frosting to spread to the edges.