Preheat the oven to 350F. Line two rimmed baking sheets with parchment paper. Drain the chickpeas, reserving 1/4 cup fo the liquid from the can (aquafaba coming at you!), rinse them, then add them to the bowl of a food processor. Process the chickpeas until they are very finely chopped, stopping a couple of times to scrape down the bowl.
Add the peanut butter, reserved aquafaba, and vanilla and blend until smooth; if the mixture is too thick for your food processor to handle, don't stress- just continue mixing by hand.
Transfer the mixture to a large bowl, add the brown sugar, and stir until the ingredients are well combined and smooth. Stir in the flour until well combined. The dough will be soft and oily, but you should be able to roll it into a ball; if you are unable to do so, add more flour, 2 tablespoons at a time, until you get there.
Place the granulated sugar in a small bowl. Using your hands, roll about 2 tablespoons of the dough into a ball, roll it in the sugar, and place it on one of the prepared baking sheets. Repeat this process until all the dough has been used, placing the balls about 1 inch apart. Use a fork to lightly press down on each ball, flattening the cookies to about 1/2 inch thick and creating a crisscross pattern. If your fork sticks to the batter, dip it in water before creating the crisscross on each cookie.
Bake the cookies until they are mostly firm and lightly browned- 17 to 22 minutes. Transfer to a cooling rack to cool completely.