Heat oven to 200°F. Line a two baking sheets with parchment paper or silicone baking mats.
Add 1/2 cup liquid from canned chickpeas, 1/4 teaspoon vanilla extract, and 1/8 teaspoon cream of tartar to the bowl of a stand mixer (or a large bowl).
Beat on high speed and slowly add 1/3 cup granulated sugar while the mixer is running. Continue beating until the mixture forms stiff peaks (about 6-7 minutes).
Pipe or spoon the meringue into small dollops about 1 inch apart onto your prepared baking sheets. Sprinkle gently with sprinkles, if desired.
Bake for 1.5-2.5 hours. The meringues will not brown, or really look any different when they are done. To tell if they are done, carefully remove one cookie and allow it to cool. It is done when it is crisp and dry all the way through (though some people like them chewy in the center). If you are looking for that chewy center, be sure to start testing them at 1.5 hours. If you like them dry all the way through, or make them large, they will need to cook longer. Store in an airtight container as soon as they are cool. They are best eaten quickly, especially if it's humid. They will begin to soften quickly in the humidity.
Notes
Make sure you're using canned chickpeas that don't have any flavoring added to them. Ideally, use no salt added chickpeas, but salted ones work too.