In a medium bowl, whisk together flour, cocoa, salt and baking powder.
In a separate, larger bowl, beat the butter until light and fluffy. Add sugar and continue beating until it's well incorporated. Then add egg, water, and vanilla and beat for at least 2 minutes, until the mixture has lightened both in color and texture. Gently mix in the dry ingredients.
Using clean hands, shape the dough into a flattened disk. Wrap in plastic wrap and refrigerate for 3 to 4 hours, or overnight. This dough is very soft, so it's imperative that it's been chilled before you roll it out.
Preheat oven to 325°F. Lightly grease (or line with parchment or silpats) two or three baking sheets.
On a clean, heavily floured work surface, roll the dough to a ⅛-inch thickness, and use a round cutter to cut it into 2¼ inch circles. Place the cookies on the prepared baking sheets. They won't expand a great deal, so you don't need a lot of space between them.
Bake the cookies for 17 to 18 minutes. (Watch carefully; it's difficult to tell when they're done, as they're so dark you can't see if they're brown, but when you start to smell them they're probably done. If you smell even a whiff of burning, remove them from the oven immediately.) Transfer the cookies to a rack and cool them completely.
Notes
You may use regular cocoa, but Dutch-process will give you a darker, more chocolaty cookie. You can also use ½ teaspoon of black food coloring to get the desired dark chocolate effect.
You can use these cookies to frost, fill or as decorations on a cake. They can also be served as "tea" cookies by themselves.