Preheat the oven to 225°. Line a baking sheet with parchment paper. In a bowl, preferably copper, beat the egg whites on medium speed until frothy, 2 to 3 minutes. Gradually add 1 1/2 tablespoons of the granulated sugar and beat for 1 minute. On high speed, beat in the remaining 3 tablespoons sugar; beat until stiff and glossy, about 2 minutes.
In a bowl, sift the confectioners' sugar with the cocoa and gently fold into the meringue until incorporated. Transfer to a pastry bag fitted with a large plain or star tip and pipe out two dozen 2 1/2-inch-long swirls, spacing them 1 inch apart.
Bake the meringues in the middle of the oven for about 1 1/4 hours, until the swirls are dry and puffed. Turn off the heat and leave the meringues in the oven for 10 more minutes. Let cool on the baking sheet, then remove them from the paper.