Place the oven racks in the upper and lower third positions. Preheat oven to 300 degrees F. Line two large baking sheets with parchment paper or a silpat mat and set aside.
In the bowl of a food processor (mini if possible), combine the hazelnuts, chocolate, and espresso powder. Pulse until finely ground. Set aside.
In a medium bowl, sift together the powdered sugar and cocoa powder. Set aside.
In a stand mixer with the whisk attachment or a large mixing bowl, whip the egg whites and salt on medium speed, until the whites are no longer clear. (Ensure your mixing bowl is perfectly clean and dry, or the whites will not whip properly.) Increase the speed to medium-high and continue to whip, adding the granulated sugar 1 tablespoon at a time as you go. Continue whipping until the whites are firm and hold stiff peaks. They should be very shiny. Beat in the vanilla extract.
With a large rubber spatula, gently and quickly fold in the powdered sugar mixture, until most streaks are gone, trying to deflate the egg whites as little as possible. Lightly fold in the chocolate-hazelnut mixture, just until combined.
With a small ice cream scoop, drop the meringues by rounded tablespoons 2 inches apart on the prepared baking sheets. Bake for 10 minutes, then without opening the oven door, reduce oven temperature to 200 degrees F and continue baking for 1 additional hour.
Remove the baking sheets from the oven, then let the meringues stand at room temperature on the baking sheets. Carefully pull the meringues off of the baking sheet and serve.
TO STORE: Keep leftover chocolate meringue cookies in an airtight container at room temperature for up to 2 weeks. Do not refrigerate as this can cause the meringue cookies to become soft and sticky.
TO FREEZE: Meringue cookies may be kept in the freezer for several months. Thaw at room temperature before serving.