Preheat oven to 200 F (90 C). Line a large baking sheet with parchment paper or a silicone baking mat. For exact measurements, draw small ½-2/3 inch circles on parchment paper. I prefer to just eyeball it and make different sizes for a more natural look.
Add the egg whites to the bowl of a stand mixer fitted with whisk attachment. Whip until foamy, about 1 minute. Then, add the cream of tartar and increase to medium high speed for another minute or until soft peaks form.
Turn speed down to medium low and slowly pour in the sugar. Increase speed to medium high for 3-4 minutes, whipping until stiff peaks form. The meringue should be thick and glossy.
Transfer meringue to a large piping bag fitted with a ¼ inch round piping tip.
To pipe the caps, hold the pastry bag upright and close to the parchment paper. With even pressure from the top of the bag, pipe 1.5 inch or similar sized rounds that are about ½ inch high. Dip you fingertip in water and level out any tips.
To pipe the stems, hold the pastry bag upright and close to the parchment paper. Using even pressure form the top of the bag, make small cylinders, by gently squeezing the meringue out onto the pan and lifting while releasing pressure. The base of the stem should be the same thickness as the piping tip and get smaller as you lift the bag. You may have a tip and thats ok. I use the tip for assembly.
Place pan on the middle rack of the oven and bake for 2 hours. Turn off the oven and let the meringue cool completely. (about 45 minutes) They should be dry and crisp.
Melt chocolate in a double broiler or using a microwave safe bowl, heating and stirring in 30 second intervals until smooth.
Carve a small hole in the center of the bottom of each mushroom cap. (Make sure not to punch through the dome.) Dip the tips of the stems in melted chocolate and connect the two. If your tips are too pointy, just shave then down to desired levelness.
Place mushrooms on a plate while the chocolate sets.