1. Line two large insulated baking sheets with parchment paper, or line two regular baking sheets and put each one on top of another baking sheet. Fit a large pastry bag with a plain 3/8 inch or 1/2 inch tip. Set these aside for the moment.
2. If you've got almond powder, just sift it with the confectioners sugar and cocoa. If you're starting with almonds, place the almonds, sugar, and cocoa in the work bowl of a food processor fitted with the metal blade and process until the mixture is as fine as flour, or at least 3 minutes. Although the almonds may look as though they're pulverized after a minute or so, they won't be: The nuts really need 3 to 5 minutes to be ground to a powder or flour. When the almonds are ground, using a wooden spoon, press the mixture through medium strainer.
3. For this recipe to succeed, you need 1/2 cup of egg whites, which means using 3 large egg whites plus part of a fourth white. Once the eggs are measured, they need to be brought to room temperature so they can be beaten to their fullest volume. To keep the eggs warm, run the mixer bowl under hot water. Dry the bowl well, pour the whites into the bowl and fit the mixer with the whisk attachment.
4. Beat the egg whites at low to medium speed until they are white and foamy. Turn the speed up to high and whip them just until they are firm but still glossy and supple - when you lift the whisk, the whites should form a peak that drops just a little. Leave the whites in the mixer bowl or transfer them to a large bowl and, working with a rubber spatula, fold the dry ingredients gently into the whites in three or four additions. Don't worry if the whites deflate and the batter looks a little runny - that's just what's supposed to happen. When all the dry ingredients are incorporated, the mixture will look like a cake batter; if you lift a little with your finger, it should form a gentle, quickly falling peak.
5. Spoon the batter into the pastry bag and pipe it out onto the prepared baking sheets. Pipe the batter into rounds about 1 inch in diameter, leaving about an inch between each round. When you've piped out all the macaroons, lift each baking sheet with both hands and then bang it down on the counter. Don't be afraid - you need to get the air out of the batter. Set the baking sheets aside at room temperature for 15 minutes while you preheat the oven.
6. Center a rack in the oven and preheat the oven to 425F.
7. You should bake these one pan at a time, so dust the tops of the macaroons on one pan with cocoa powder and slide one of the sheets into the oven. As soon as the baking sheet is in the oven, turn the temperature down to 350F and insert the handle of a wooden spoon into the oven to keep the door slightly ajar. Bake the macaroons for 10-12 minutes, or until they are smooth and just firm to the touch. Transfer the baking sheet to a cooling rack and turn the oven heat back up to 425F.
To remove the macaroons from the parchment - they should be removed as soon as they come from the oven - you will need to create moisture under the cookies. Carefully loosen the parchment at the four corners and lifting the paper at one corner, pour a little hot water under the paper onto the baking sheet. The water may bubble and steam, so make sure your face and hands are out of the way. Move the parchment around or tilt the baking sheet so that the parchment is evenly dampened. Allow the macaroons remain on the parchment, soaking up the moisture, for about 15 seconds, then peel the macaroons off the paper and place them on a cooling rack.
8. When the oven is at the right temperature, repeat with the second sheet of macaroons. Remove from the parchment as directed above and let cool.