Preheat oven to 175 degrees. Fill a medium saucepan 1/4 full with water. Set over medium heat; bring water to a simmer.
Combine egg whites, sugar, and cream of tartar in the bowl of an electric mixer, and place over saucepan. Whisk constantly until sugar is dissolved and whites are warm to the touch, about 3 minutes; rub the mixture between your fingers to test.
Transfer bowl to mixer stand fitted with the whisk attachment, and whip, starting on low speed and gradually increasing to high, until meringue is cool, and stiff glossy peaks form. Add vanilla; mix until combined. Use immediately.
Place in a pastry bag fitted with a 1/2-inch round tip. Line two baking sheets with parchment paper. Pipe meringue, forming mushroom caps 1/2 inch in diameter. Pipe a stem shape for each cap. Place baking sheets in oven until meringue is dry in center, 1 to 2 hours.
Poke a small hole in the center of each cap using a paring knife. Insert the pointed end of each stem into hole in the cap, forming mushrooms. Meringue mushrooms should be kept in an airtight container in a cool, dry place. Just before using, dust lightly with cocoa powder.