Preheat the oven to 400°F. Have ready a nonstick cookie sheet, or line a regular cookie sheet with a silicone mat.

In a bowl, combine the confectioners’ sugar, cocoa powder, and water and whisk until well blended, add the butter and whisk just to combine. Using a rubber spatula, fold in the flour just to incorporate. Do not overmix, or the batter will shrink as the cookies bake. If lumps form, carefully break them up with the spatula and incorporate them into the batter. (The batter can be made to this point, covered, and refrigerated for up to 1 week, return to room temperature before proceeding.)

Using a small offset spatula, spread the batter into circles about 2 inches in diameter and 1/8 inch thick on the prepared cookie sheet, spacing them about 2 inches apart. Sprinkle some chopped nuts in the center of each circle. Have a clean rolling pin or a bottle or two at hand.

Bake for about 10 minutes, or until just set. Remove from the oven and let rest for 30 seconds. Using an offset spatula and working quickly, lift the cookies one at a time from the pan and drape, nut side up, over the rolling pin. Allow the cookies to cool on the rolling pin for about 3 minutes, so they will hold their shape. If they cool on the pan before you get a chance to drape them, place the pan back in the oven for about a minute to soften them. Transfer the cookies to a wire rack and repeat with the remaining batter. Serve immediately, or store in an airtight container at room temperature for up to 5 days.