125ml of aquafaba is 1/2 cup, if that's easier for you to measure.
Put your aquafaba into the bowl of a stand mixer. Whack your mixer up to the maximum, using the whisk attachment if you have one, and let it go for around 20 minutes.
You want to get it to a stiff peak, and yes you can test this by holding the bowl upside down. If it stays put then you have the right consistency. If it starts to move as you tilt the bowl then keep on mixing! (Please keep mixing--I don't want to be held responsible for egg-white hair :D)
During the next stage of mixing, you can put your oven on to 110C/230F, and prepare two baking sheets by covering them with baking parchment.
Once you've ensured your egg whites are at the right consistency, put your mixer on again and add the sugar a spoon at a time--don't chuck it all in at once. You need to keep on whisking until the sugar is no longer grainy. You can add your vanilla during this stage too.
Use a small amount of mix on each corner of the baking parchment to make sure it sticks to the tray.
You can either spoon your mixture onto the baking sheets or pipe them. I usually use a heaped ice cream scoop, to get the mix out and a spoon to smooth. This makes meringues that are about as big as the palm of your hand (depending on how big your hands are of course!). Leave plenty of room between each one as they will spread a fair bit.
Put them in the oven for 2 hours. If you can pick one off the tray easily and the top and bottom has a crisp shell then they are done. Either remove straightaway, or if you have time then just turn the oven off and let them cool gradually in the oven.