Preheat the oven to 200°F. Line 2 large baking sheets with parchment paper.
Wipe down the bowl of your stand-mixer and balloon whisk attachment with vinegar and a paper towel. Removing any fat or oil residue is critical to ensure that the meringue does not deflate.
Add the aquafaba and vinegar to the bowl, and whip on high until stiff peaks form. The meringue should cling to the bowl when it's turned upside down, and should form a peak which keeps its shape when the whisk is removed and turned upside down.
Add the sugar to the meringue, a few tbsp at a time, keeping the mixer on high. At this point, beat only until the sugar is incorporated. While aquafaba can be beaten forever (unlike egg white meringue which can become dry and break), once the sugar is added to aquafaba it can deflate the meringue once the sugar is completely dissolved during over-beating.
Spoon the meringue into a piping bag fitted with a 3/8"-1/2" round tip. Start by creating 25 stems and 25 caps.; you may have some left over for more at the end. To make the domes, pipe 1/2" above the baking sheet until you have a diameter of about 1.5"-2"; turn the tip quickly at the height of the dome and then lift quickly. Use a finger dipped in water to smooth the point or bump on the dome. For the stems, pipe and then lift until you have a stem about 1-1.5" high and then quickly lift to release the meringue, creating a "kiss" shape. Create some variation in the sizes, but take care not to make the stems too high or they will fall over. Dust the mushroom stems and caps with a bit of cocoa powder.
Bake the meringues for 1.5 hours, rotating the baking sheets halfway through. At the end of the baking time, the meringues will be hard but should not change color. Turn the oven off but leave the meringues inside with the door closed until the oven is completely cool. The meringues can be stored there until you're ready to assemble the mushrooms.