Preparation In electric mixer, beat butter and sugar at high speed until fluffy, about 5 minutes. Add egg, baking soda, and salt and beat at medium speed until blended. Add cocoa powder and mix at low speed until incorporated. Add flour and mix at low speed until just combined. Divide dough in half, form into 2 disks, and wrap in plastic wrap or waxed paper. Chill until firm, at least 1 hour or up to 2 days. Arrange racks in upper and lower thirds of oven and preheat to 350°F. Line 2 heavy large baking sheets with parchment paper. Remove 1 dough disk from refrigerator. On lightly floured work surface, roll out dough to 1/4- to 1/8-inch thickness. Using 3- to 4-inch snowflake cookie cutter, cut out cookies; transfer with spatula to baking sheets. Gather and reroll scraps and cut out additional cookies. Chill cookies 10 minutes. Bake until somewhat firm to the touch, about 10 minutes. (Do not overbake or cookies will be bitter.) Cool on pans 2 minutes, then transfer to racks and cool completely. Repeat with remaining dough. To decorate, lay lacy doily on top of cookies and dust with confectioners' sugar.
Preparation In electric mixer, beat butter and sugar at high speed until fluffy, about 5 minutes. Add egg, baking soda, and salt and beat at medium speed until blended. Add cocoa powder and mix at low speed until incorporated. Add flour and mix at low speed until just combined. Divide dough in half, form into 2 disks, and wrap in plastic wrap or waxed paper. Chill until firm, at least 1 hour or up to 2 days. Arrange racks in upper and lower thirds of oven and preheat to 350°F. Line 2 heavy large baking sheets with parchment paper. Remove 1 dough disk from refrigerator. On lightly floured work surface, roll out dough to 1/4- to 1/8-inch thickness. Using 3- to 4-inch snowflake cookie cutter, cut out cookies; transfer with spatula to baking sheets. Gather and reroll scraps and cut out additional cookies. Chill cookies 10 minutes. Bake until somewhat firm to the touch, about 10 minutes. (Do not overbake or cookies will be bitter.) Cool on pans 2 minutes, then transfer to racks and cool completely. Repeat with remaining dough. To decorate, lay lacy doily on top of cookies and dust with confectioners' sugar.