Place oven racks to divide in thirds and preheat to 225 °F. Line two cookie sheets with aluminum foil.
Using stand mixer, at slow speed beat egg whited until foamy. Add salt and cream of tartar. Increase speed to moderate and beat until they begin to hold a soft shape. While continuing to beat, add sugar one rounded tablespoonful at a time, allowing about 30 seconds between additions. Once sugar has been added, mix in vanilla. Increase speed to high, beating about 7 - 8 minutes, until meringue is very stiff and sugar is dissolved when tested by rubbing between two fingers.
To prevent aluminum foil from shifting while working, place a dot of meringue between foil and cookie sheet at each corner. Fit a large pastry bag with a plain round tube, size #8 (5/8" diameter. Transfer all meringue to pastry bag; close top by rolling or twisting.
To shape mushroom stems, a small sharp knife in a glass of water is needed. Using first baking sheet, form stems by gently squeezing bag while raising it straight up. Form stem a bit wider for support and try to keep stem as straight as possible. Stems should be about 1 - 1 3/4" high. Take knife, shake off excess water (don't dry), and cut meringue away from tube. Place stems about 1/2 - 1 inch apart on baking sheet. Some will fall over, so make extras to have enough.
Using second baking sheet, create mushroom caps by holding pastry bag straight up and close to foil. Space 1/2" apart. They should be about 1½- 1¾" wide and ¾" high. Sharply twist, release pressure on bag, and slowly move bag off to side of cap to avoid leaving a peak and make cap as smooth as possible.
Strain cocoa lightly over stems and caps.
Bake stems on top rack of oven and caps on bottom rack for about 1 hour, longer for larger meringue, until they may be easily lifted from foil and bottoms are firm to touch. Do not allow to brown. Turn off oven and prop door open slightly to dry out more.
Remove meringues from foil. If tops of stems are not flat, immediately use finely serrated knife to saw off tops creating a flat surface parallel with base. Store in a dry environment until ready to glue together with chocolate.