Add all the dry ingredients to a food processor (cocoa powder, flour, sugar, baking soda and salt). Pulse until they are blended thoroughly and are an even texture and color.
Scatter the butter slices on top of the dry ingredients. Run the processor until the butter is incorporated and forms an even texture. It will appear a bit sandy and rocky.
Mix the vanilla into the half and half. Re-start the food processor and slowly pour the liquid into the feed tube. At this point, the dough will come together and begin to form heavy clumps. It will not mix entirely. It is ok to shut off the food processor at this point, especially if it sounds like it is straining.
Dump the cookie dough onto a clean work surface. Knead it until it comes together nicely and is an even color and texture. It will be dark and glossy.
Form the finished dough into a ball and divide in half.
Using your hands, roll each half into a cylinder. Mine were approximately 1 3/4" diameter. Wrap them securely in plastic wrap and refrigerate at least 2 hours or overnight if you'd like.
After refrigeration, remove the cylinders and slice each one into approximately 1/8" discs. The dough is very solid and slices easily with a sharp blade. Place the rounds on a baking sheet lined with parchment. My two cylinders made approx. 48 slices.
Place the baking sheets in a preheated 350 degree oven. Bake for 12 minutes. If you bake both sheets at the same time, rotate the sheets and switch racks half way through for even cooking. They are done when the discs are flat and there is no puffiness on the rounds.
Place the baking sheets on a cooking rack for 5 minutes before removing the cookies with a spatula. This will firm them up and they will keep their shape. You may then remove the cookies from the baking pan and place them directly on the cooling rack. They will crisp up as they cool. Once cooled they are ready to be layered and covered with whipped cream.
