Make the cookies: 

1. In a large bowl, cream together the softened butter with the white sugar and salt until light and fluffy. Add the egg and beat until fully incorporated.
2. In another bowl, sieve the flour, cocoa powder, and baking soda. Mix to combine well.
3. Add the dry ingredients to the wet ingredients, and mix with a spatula together until combined.
4. Place a large piece of plastic wrap on the counter and transfer the dough on top. With your hands, form a dough ball or square. Wrap it with the plastic wrap and refrigerate to chill for 1 hour.
5. Preheat the oven to 325˚F (160˚C) and line a baking sheet with parchment paper.
6. Remove the dough from the fridge, and with a knife, divide the dough ball into 2 pieces. Return the other half, wrapped, to the fridge to keep chilled while you roll and cut out the first batch of cookies.
7. Place half of the dough between two sheets of parchment paper and roll it to ¼-inch (½-cm) thickness.
8. Using a small round cookie cutter (of 1 ½ to 2 inches in diameter), cut out as many cookies as you can and place them directly on the parchment-lined baking sheet.
9. Pack together and re-roll out any scraps to cut additional cookies. Repeat this process with the other half of the remaining dough from the fridge.
10. Bake in a preheated oven for 15 minutes. Remove from the oven and transfer cookies to a cooling rack to cool completely.

Make the filling & assemble cookies: 

1. Combine butter, powdered sugar, and vanilla in a medium mixing bowl. Beat together until light and fluffy.
2. Assemble the cookies by spreading a generous scoop of the icing onto one of the fully cooled cookies and sandwiching it with another. Give it a light squeeze and scrape any excess off to clear and even out the sides.