Preheat your oven to 175°C (347°F) and line the base of 2 large baking trays with a sheet of parchment paper. (You may need to bake them in batches if your trays are on the smaller side).
Add the vegan butter and sugar to a large mixing bowl or the bowl of a stand mixer and whisk for 3-4 minutes until light and fluffy.
Slowly pour in the aquafaba whilst whisking until combined. Whisk in the vanilla extract.
In a medium bowl, stir together the flour, baking powder, and salt. Sift them into the bowl with the butter and sugar. Add in the soy milk. Stir the ingredients together using a spatula until just combined.
Transfer the cookie dough to a piping bag and snip off the tip, or use a reusable piping bag with a medium tip. Pipe the dough onto the baking sheet in even mounds, about 1 teaspoon in volume for small wafers, or 1.5 teaspoons for larger wafers. Make sure you leave 1.5-2 inches of space around each mound. If you have any batter left over after filling the trays, place it in the fridge until ready to bake.
Bake until they are evenly golden brown, then remove from the oven and let them sit on the baking tray to cool for about 5 minutes. Next, carefully slide the sheet of parchment paper with the cookies off of the tray and onto a cooling rack. Cool for another 15-20 minutes until they reach room temperature before serving.