Place the almond paste and sugar in a large mixing bowl and beat with an electric mixer on medium-high speed until the almond paste is softened and the sugar well incorporated, about 5 minutes. Add the cocoa powder and blend just until combined.
Add the egg whites a little bit at a time, incorporating fully after each addition. Egg whites are difficult to pour in small amounts, so hold a rubber spatula against the rim of the bowl and use it to "cut" the egg whites as they are poured. If you add the egg whites all at once, the mixture will be lumpy because the difference in consistency between the egg whites and the almond paste mixture is too great. Use a rubber spatula to scrape down the sides of the bowl as needed. You may or may not need all of the egg whites depending on the moistness and age of your almond paste. Stop mixing when the mixture reaches a consistency soft enough to pipe (like toothpaste).
Place the batter in a pastry bag fitted with a 1/2-inch plain tip. Pipe 1-inch mounds onto a parchment paper-covered baking sheet. It will be easier if you hold the pastry bag at a slight angle and allow the tip to touch the parchment as you start to pipe. Once you have formed the mound, stop squeezing and lift the tip straight up, leaving a small tail on the top of each mound. Space the macarons about 1-inch apart to allow for spreading. Pipe carefully: Your macarons will look nicest when they are sandwiched together if they are all the same size.
Immediately before placing them in the oven, liberally sprinkle granulated sugar over the macarons. This will give them a nice crust that will keep the inside moist and chewy. Bake until golden brown, 8 to 10 minutes. The top of each macaron should be very finely cracked, a characteristic for which they are known. If overbaked, the macarons will be dry and crunchy.
Remove the baking sheet from the oven and immediately pour 1/4 cup of water onto the baking sheet under the parchment paper. Be careful: If you get any water on the macarons, they will be soggy. You will need to tilt the baking sheet to spread the water evenly. Let it sit for 2 minutes. The water will loosen the macarons from the paper. Remove the macarons from the paper 2 at a time and stick them together, matching the flat sides. Do not put them back on the hot, wet baking sheet or they will become soggy.
The macarons can be stored in an airtight container at room temperature for up to 3 days or well wrapped in the freezer for up to 1 week. Unwrap them before bringing back to room temperature, or the condensation will make them soggy.