Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.

In a medium bowl, whisk together the flour, cocoa powder, baking soda, and salt. Set aside.

In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy, about 2-3 minutes.

Add the egg and vanilla extract to the butter mixture, mixing until well combined.

Gradually add the dry ingredients to the wet ingredients, alternating with the milk, and mix until just combined.

Using a tablespoon or a cookie scoop, drop rounded tablespoons of batter onto the prepared baking sheets, leaving space between each for spreading.

Bake in the preheated oven for 10-12 minutes, or until the tops spring back when lightly pressed. Remove from the oven and let cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.

While the cookies are cooling, prepare the filling. In a mixing bowl, beat together the peanut butter, softened butter, powdered sugar, and vanilla extract until smooth. If the filling is too thick, add heavy cream one tablespoon at a time until desired consistency is reached.

Once the cookies are completely cool, spread a generous amount of the peanut butter filling on the flat side of one cookie and sandwich it with another cookie. Repeat with the remaining cookies.

Serve immediately or store in an airtight container in the refrigerator for up to 3 days.