Combine butter, sugars and vanilla in the bowl of an electric mixer and beat on medium speed until light, about 5 minutes, scraping bowl and beaters occasionally. Beat in the egg whites, one at a time, beating smooth after each addition.
While the mixture is beating, sift the cocoa with the flour and salt. Stop mixer, scrape down bowl and beaters and add dry ingredients. Mix on low speed until incorporated.
Scrape the dough out onto a piece of plastic wrap. Cover with another piece of wrap and press the dough into a rough disk. Refrigerate the dough until it is firm -- several hours or overnight.
About 20 minutes before you intend to bake the cookies, set a rack at the middle level of the oven and preheat to 350 degrees.
Divide the dough into 3 parts and roll one at a time on a lightly floured work surface into a 6-inch square. Cut the dough with a fluted or plain round cutter into nine 2-inch cookies and place them on the prepared pan. Continue with the remaining dough. After rolling all the dough, press the scraps back together and make about 9 more cookies. Pierce the cookies several times with a fork and sprinkle them lightly with granulated sugar.
Bake the cookies about 20 minutes, until slightly puffed and firm. Cool the cookies on the pan.
Serve with any creamy or plain dessert, or ice cream. They're also great by themselves. Storage suggestion: Keep the cookies between layers of waxed paper in an air-tight tin or plastic container
Recipe Courtesy of Nick Malgieri (This great recipe comes from my friend Marie Ostrosky, one of the backstage chefs at TVFN)