In a medium bowl, whisk together the butter and granulated sugar until well combined. Whisk in the vanilla and chocolate. Add the egg and whisk until thoroughly incorporated.
In another medium bowl, stir together the flour, cocoa powder, salt, and baking soda until well mixed. Using a wooden spoon or a fork, stir the flour mixture into the chocolate mixture. The dough will start to seem as though it's too stiff, too floury. You may find it easier to switch to mixing it with your hands until the dough comes together and achieves the consistency of Play-Doh. Let the dough sit at room temperature for about 1 hour to firm up.
Transfer the dough to a 15-inch square sheet of parchment or waxed paper. Using your hands, shape the dough into a log about 10 inches long and 2 to 2 1/2 inches in diameter. Place the log at the edge of the paper and roll the paper around the log. With the log fully encased in paper, roll it into a smoother log no more than 2 1/2 inches in diameter. Refrigerate for at least 2 hours or until firm. The log may settle and sink a bit in the fridge; if you like, re-roll it every 15 minutes or so to maintain a nice round log. If not, your cookies will be more oblong than round, which is not a bad thing taste-wise, though they won’t look like the famous packaged cookie. (The dough can be wrapped in plastic wrap and refrigerated for up to 1 week or frozen for up to 1 month. If the dough is frozen, thaw overnight in the refrigerator before proceeding.)
Position a rack in the center of the oven and preheat the oven to 325°F (163°C). Butter a baking sheet or line it with parchment paper.
Slice the dough log into 1/4-inch-thick slices. Place the slices about 1 inch apart on the prepared baking sheet.
Bake for 20 to 25 minutes, or until the cookies are firm to the touch. Check them frequently after 15 or 16 minutes, poking them in the middle; as soon as they feel firm to the touch, remove them from the oven. You can’t judge by color because they start out black. Place the baking sheet on a wire rack and let the cookies cool on the baking sheet.