Preheat oven to 225 degrees. Prepare 2 baking sheets by lining with parchment paper. Prepare a pastry bag fitted with a small number 6 plain tip.
In the bowl of a stand mixer or using a hand mixer on medium-low speed, beat together the egg whites and cream of tartar until foamy.
Continue to beat, slowly adding granulated sugar. Increase speed to high and beat until soft peaks form and the mixture holds stiff shiny peaks. Sift powdered sugar over the egg white mixture and fold in until well blended, using a rubber spatula.
Scoop the mixture into the prepared pastry bag. On the first baking sheet, pipe 48 mushroom stems by piping them from about 1/2 inch at the base of the stem to about 3/4 inch at the tip, spacing them 1/2 inch apart.
Pipe the tops of the mushrooms on the other baking sheet by piping 48 mounds about 1 1/4 inch wide and about 3/4 inch tall, spacing them also 1/2 inch apart. Remove any pointy tips by gently rubbing with a slightly damp finger. Dust mushrooms with cocoa.
Place baking sheets in the oven and bake until firm enough to be removed from sheet, about 50 to 55 minutes. Place sheets on counter (make sure to protect counter by placing on a trivet) and flip mounds so the flat sides are up.
With the tip of a knife, gently make a small hole in the bottom of the mound. Pipe a small amount of reserved meringue into the hole and insert the stems tip first. Repeat with remaining mounds. Place sheets in oven and bake until completely dry, about 15 minutes. Allow to cool completely on baking sheets.