Combine egg whites with cream of tartar in bowl of an electric mixer. Beat on medium speed until soft peaks form. Gradually sprinkle in sugar, beating at high speed until mixture is very stiff and dull looking.
Scrape meringue mixture into pastry bag. Pipe round, button shapes to make mushroom "caps". Pipe pointed "kiss" shapes about one inch tall to make "stems". Dust with cocoa. Bake two hours in 200 degree oven until crisp and completely dry. Assemble the mushrooms: Place chocolate in a small bowl. Set bowl in a skillet of barely simmering water. Immediately turn off heat and stir chocolate until melted and smooth. Spread a little melted chocolate on the flat side of each meringue mushroom "cap". Use a sharp knife to cut off and discard the pointed ends of meringue "stems". Attach stems to caps while chocolate is still soft. Set assembled mushrooms aside until the chocolate has dried and caps and stems are "glued" together. Meringue mushrooms may be made 3-4 weeks in advance and stored in an airtight container.