Combine powdered sugar and cocoa powder. Grease bottom and sides of a 13x9 inch baking pan; dust with sugar mixture, reserving the rest for later.
Grease a large mixing bowl. Pour 1/4 cup cold water into bowl; sprinkle with gelatin. In a saucepan, cook 1/4 cup water, sugar, and corn syrup over medium heat, stirring constantly, until sugar is dissolved, about 2 minutes. Bring to a boil; continue to cook until the mixture registers 240-degrees on a candy thermometer, about 10 minutes. Pour over gelatin mixture.
Beat with an electric mixer on high speed until it become thick and white and triples in size - this can take anywhere from 10 to 15 minutes. Meanwhile, beat egg white until still peaks form, Stir the beaten egg whites into the gelatin mixture until just combined. Stir in 2 tablespoons cocoa powder.
Pour marshmallow into prepared baking pan; sift powdered sugar mixture over top. Chill until firm, at least 3 hours.
Run a knife around the edge of the pan; invert onto cutting board and remove pan. Use a large, oiled knife to cut the marshmallows into 2-inch squares. Dust cut edges with sugar/cocoa powder. Store in an airtight container either in the refrigerator or at room temperature.