In a large bowl with an electric mixer at low speed, beat the egg whites until frothy. Add the cream of tartar and increase the speed until soft peaks form. Start adding the sugar slowly. Beat until glossy stiff peaks form.
Place the meringue in a piping bag or large zip-lock bag and push the mixture toward one corner, folding the other corner over, then twisting, allowing you to control the meringue. Cut off just the very tip of the exposed corner so the meringue can exit the bag. Then try it out by dotting four small beads of meringue at the corners of a cookie sheet. Set a sheet of parchment paper over the top; the meringue beads will provide a bond to hold the paper in place.
Make the mushroom caps by holding the bag over the parchment paper and push until a 1-inch mound of meringue forms. Wet the tip of your finger with water and gently round off any peaks to make a smooth surface.
For mushroom stems, form peaks on smaller mounds of meringue by pulling the bag up and away from the surface as you push.
Bake them in a 200° oven for an hour, and then turn oven temperature down to 175 and leave them until they’re completely dry to the touch.
Melt the chocolate chips in a glass microwave-safe dish in the microwave for about one minute or until melted. Once cool, you can coat the bottom of the mushroom caps with dark chocolate, let them set, and then coat them again with white chocolate. Once the white chocolate is set, you can scratch in the mushroom gills using a toothpick, and attach the stem using a little more white chocolate.
Or, if not coating the bottom of the mushroom caps, make a hole smaller than a pea in the bottom of a mushroom cap with a toothpick or skewer. Dip the tip of the stem in the melted chocolate and press into the hole in the cap. Allow the chocolate "glue" to harden (it only takes a minute). Place the mushroom upright on its stem and dust the cap lightly with cocoa powder.