Preheat the oven to 200°F and line two baking sheets with parchment paper.
Beat the chilled aquafaba and cream of tartar until the mixture is very foamy and begins forming soft peaks.
Add the superfine sugar 1 tablespoon at a time while continuing to beat. Once all the sugar has been incorporated, beat for 6 to 8 minutes longer, until the meringue is thick, glossy, and holds stiff peaks.
Beat in the vanilla and salt just until incorporated. Spoon or pipe small mounds of meringue onto the prepared baking sheets.
Bake for 1 hour and 30 minutes to 1 hour and 45 minutes, until the cookies feel dry and release easily from the parchment.
Turn off the oven and leave the meringues inside with the door closed for 1 hour. Remove and cool completely before storing in an airtight container.