Sift the cake flour and cocoa powder together in a small mixing bowl and set aside. Place the egg whites in a large mixing bowl and whip until foamy with an electric mixer set on medium speed. Make a French meringue by adding the sugar 1 tablespoon at a time. When you whip egg whites, add the sugar slowly to allow the whites to gain some volume. When you have volume, add the rest of the sugar. Increase the mixer speed to medium-high and whip to stiff but not dry peaks, about 5 minutes. When the whites are slightly stiff, reduce the mixer speed to low to allow even more air to be incorporated without over whipping the egg whites. Let the egg whites continue to whip for about another 2 minutes. Stop whipping them if they begin to look dry or separated.
Very gently, fold the egg yolks into the whipped egg whites with a rubber spatula until they are partially incorporated. Carefully fold the sifted mixture into the egg mixture. It is important to fold as gently as possible to avoid deflating the batter. Remember to fold all the way to the bottom of the bowl to fully incorporate both mixtures.
Place the batter in a pastry bag fitted with a 3/4-inch plain tip. To pipe the ladyfingers, hold the pastry bag at a slight angle and allow the tip to touch the parchment paper as you start to pipe. Squeeze gently, applying even pressure as you pipe the desired length, then stop squeezing and lift the tip straight up, leaving a small tail on the end of each ladyfinger. Pipe evenly shaped ladyfingers about 3/4-inch wide on a parchment paper-covered sheet pan. Space them about 1/2-inch apart to allow them room to spread as they bake. Dust the tops of the ladyfingers with powdered sugar to give them a nice crust.
Bake the ladyfingers until light and evenly browned, about 5 minutes. (The browning may be difficult to discern with the chocolate ladyfingers.) Remove from the oven and immediately move to a wire rack to prevent the heat of the pan from continuing to bake the ladyfingers. Set aside until ready to use. When cooled, the ladyfingers can be stored in an airtight container at room temperature for up to 2 days, or in the freezer, well wrapped in plastic wrap, for up to 2 weeks.