(Outdoor Method) Build a safe outdoor fire using lump charcoal. Be sure to keep a fire extinguisher close at hand. Wrap the chestnuts in heavy-duty foil so that they can move freely inside the foil pouch. Using a chopstick tip, poke three holes in both sides of the foil packet. Place the foil packet in the fire for 4 minutes. Flip and cook for another 3 minutes. Using tongs, remove the pouch from the fire and allow to cool to room temperature, approximately 30 minutes. Rough chop the chestnuts and set aside.
For the cookies: Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.
In a stand mixer with a paddle attachment, cream together the butter and sugar on medium speed until the mixture becomes pale yellow and well combined. Add the vanilla and egg and mix until combined, approximately 30 seconds.
Slowly add the dry ingredients from the bowl into the stand mixer on the lowest possible speed. Once the mixture starts to come together, gradually increase the speed to medium until it forms a dough-like ball. Form 20 even-sized balls and place them on the prepared baking sheets.
For the salty caramel crack: Add the sugar to a medium dry skillet and set over medium heat; the sugar will start to melt and turn a pale yellow color. Shake the pan and let it continue to melt. The sugar will start to turn golden brown and then a deep rust color--make sure to shake the pan often to mix. Once the sugar becomes a solid amber red, remove from the heat and add the cream and then the butter. Mix quickly with a soup spoon; it will start bubbling. Be careful not to touch the sugar with your hands as it is scorching hot.
While the sugar is still soft and can be drizzled, spoon it generously over the cookies. The sugar will start setting to a hard crack as it cools fully. Sprinkle some flaky sea salt on top of each glazed cookie. Let the cookies fully cool before serving.