In an electric mixer, beat the butter and the sugar with a paddle attachment on low speed. Do not incorporate any air into the mixer. If you have a kitchen aid stand-up mixer, turn to "stir." It is very important to keep the speed low, so when you roll out the cookie dough, it will not crumble easily.
Add the egg and scrape until well blended.
Add the cocoa powder, then water, and scrape until well blended
Add the flour and mix until the dough comes together evenly. The finished dough should feel like Play-Doh. Do not over mix. Cover the dough with plastic, and set aside for 1 hour or until firm.
Place the dough on a long sheet of parchment paper. Use your hands to shape it into a rough log, about 10 inches long and 2 1/2 inches in diameter. Place the log at the edge of the parchment. Roll the parchment around the log. With your hands on the paper, roll the dough into a disc.
Refrigerate the dough for at least 2 hours. Place the dough between two parchment papers. Use a French rolling pin to roll out the dough between the parchment paper until the dough is a quarter-inch thin. Use a football-shaped cookie cutter to cut out cookies.
Set the oven at 325 degrees. Line 2 baking sheets with parchment paper.
Set the cookies on the baking sheets 1 inch apart.
Bake the cookies for 20 to 25 minutes, checking them often after 15 minutes. Flip the cookies and keep baking them until they are firm when touched in the center.
Cool completely on the sheets.