Position oven rack in the middle position and preheat to 285°F. Line two large baking sheets with parchment paper.
Sift together the confectioners' sugar, both cocoa powders, and espresso powder through a fine-mesh sieve into a medium bowl. This removes any lumps and ensures a smooth meringue.
In a large, clean bowl (preferably metal or glass), beat egg whites, cream of tartar, and salt using an electric mixer on medium speed until foamy and soft peaks form, about 1-2 minutes.
With the mixer running on high speed, gradually add the granulated sugar, one tablespoon at a time, waiting 20 seconds between additions. Continue beating until the meringue is thick, glossy, and holds stiff peaks, about 2-3 minutes total. Beat in vanilla extract.
Using a large rubber spatula, gently fold the cocoa mixture into the meringue in three additions. Use a light hand and fold just until incorporated, maintaining as much air in the mixture as possible.
Pipe or spoon 1½-inch mounds onto the prepared baking sheets, spacing them 2 inches apart. Use the back of a spoon to create a slight swirl or peak on top of each meringue.
Bake for 25-28 minutes, or until the outside is dry and slightly firm to the touch but still gives slightly when pressed. The interior should remain soft and marshmallow-like.
Remove from oven and let cool completely on the baking sheets, about 30 minutes. Gently peel meringues from the parchment paper.