Preheat your oven to 300°F (150°C), and if you have a convection fan in your oven, turn that on.
In a medium bowl, mix together the all-purpose flour, cornstarch (or arrowroot or tapioca starch), baking powder, baking soda, and salt, then set this aside.
Either in In a stand mixer with the whip attachment, or using a hind mixer, whip the aquafaba with cream of tartar until stiff peaks form.
Gradually add sugar, continuing to mix until the mixture becomes glossy and falls in ribbons.
Next, add the vanilla extract, olive oil, and vegan yogurt to the meringue. Mix until just combined, though the mixture won't retain its soft peaks.
Carefully fold the dry ingredients into this wet mixture in increments to avoid overmixing.
Transfer the batter to a sturdy piping bag fitted with a round nozzle. The dough will be very thick and sticky, so it will be a little hard to pipe, but trust me, it will work!
Pipe the mixture onto baking trays lined with parchment paper, forming each ladyfinger about 3 ½ inches long and 1 inch wide (8 x 2.5 cm), leaving space between them.
Dust the piped ladyfingers with icing sugar (make sure it's vegan) before baking them in the preheated oven for 30 minutes until lightly golden. Allow them to sit on the tray to set up for 5 minutes before transferring them to a cooling rack.