1. Preheat the oven to 400° and position racks in the upper and lower thirds. Line 2 baking sheets with parchment paper.
2. In a large, wide bowl, using a large rubber spatula or a handheld electric mixer, mix the confectioners' sugar with the almond flour and cocoa powder. Add 2 of the egg whites and mix until evenly moistened.
3. In a small saucepan, combine the granulated sugar with the water and bring to a boil; using a moistened pastry brush, wash down any crystals from the side of the pan. Boil over high heat until the syrup reaches 240° on a candy thermometer.
4. In another large bowl, using clean beaters, beat the remaining 3 egg whites until soft peaks form. With the mixer at high speed, carefully drizzle the hot sugar syrup over the egg whites and beat until the meringue is firm and glossy.
5. Stir one-fourth of the meringue into the almond-cocoa mixture. Using a rubber spatula, fold in the remaining meringue. Transfer the meringue to a pastry bag fitted with a plain 1/2-inch tip; pipe onto the prepared baking sheets in 1 1/2-inch mounds, spacing them about 1 inch apart. Tap the sheets and let dry at room temperature for 15 minutes.
6. Transfer the meringues to the oven and immediately turn off the heat. Bake the meringues for 5 minutes. Turn the oven on to 400° again and bake the meringues for 8 minutes, until the meringues are puffed and the tops are firm and glossy. Transfer the baking sheets to racks and let the meringues cool completely.
7. Meanwhile, in a small saucepan, combine the cream with the corn syrup and bring to a boil. Remove from the heat. Add the chocolate and let stand until melted, about 5 minutes. Whisk until smooth. Transfer the ganache to a bowl and let cool to room temperature, whisking occasionally; it will become very thick.
8. Carefully peel the meringues off of the parchment paper. Spoon the ganache into a small pastry bag fitted with a 1/4-inch tip. Alternatively, use a resealable sturdy plastic bag and snip off a corner. Pipe the ganache onto the flat sides of half of the meringues. Top with the remaining meringues and serve.