Beat together the butter and sugar until well combined. Whisk in the vanilla and chocolate. Add the egg and mix until thoroughly incorporated.

In another medium bowl, whisk together the flour, cocoa powder, salt, and baking soda until well mixed.

Add the flour mixture to the butter mixture and mix until it comes together. It will be thick and floury. Use your hands to really mix it together. It should have the consistency of play-doh.

Let the dough sit at room temperature for about 1 hour.

Transfer the dough to a 15 inch square sheet of parchment or wax paper. Use your hands to shape the dough into a log about 10 inches long and 2 1/2 inches in diameter. Place the log at the edge of the sheet of parchment paper and roll the parchment around the log. Twist the ends close, keeping the log fully encased in the parchment. Roll it into a smooth log and refrigerate for at least 2 hours, or until firm.The log may settle and sink a bit, so reroll it every 15 minutes or so to maintain the shape.

Heat oven to 325 degrees and line a baking sheet with parchment paper.

Cut the dough log into 1/4 inch thick slices. Place the slices about 1 inch apart on the baking sheet.

Bake for 20 to 25 minutes or until the cookies are firm to the touch. Check them frequently after 16 minutes, poking them in the center. As soon as they feel firm to the touch remove them from the oven.

Let cool on the baking sheet to warm or room temperature.

While the cookies are cooling, beat the butter for 30 seconds or until completely smooth. Add the powdered sugar and vanilla and beat until the mixture is perfectly smooth. Add the milk and salt and beat again. The mixture should feel a bit like putty.

Scoop 1 rounded tablespoon of the filling on the bottom of half of the cookies and top with the remaining cookies.