Prepare the pan: Line an 8×8-inch baking dish with parchment paper. In a small bowl, whisk together the powdered sugar and cornstarch. Lightly dust the bottom and sides of the pan with some of the mixture and set aside.
Whip the aquafaba: Add the aquafaba and cream of tartar to the bowl of a stand mixer fitted with the whisk attachment. Briefly whisk by hand to fully incorporate the cream of tartar. Beat on medium-high speed until soft peaks form, about 5–8 minutes.
Make the sugar syrup: Meanwhile, combine the granulated sugar and water in a small saucepan over medium heat. Heat until the syrup reaches just above the soft ball stage (235–240°F / 113–116°C). With the mixer running on low speed, slowly pour the hot syrup into the aquafaba in a thin stream, aiming between the whisk and the side of the bowl so it incorporates smoothly without splashing or sticking. Increase the mixer speed to medium-high and continue whipping until the mixture becomes thick, glossy, and reaches stiff peaks, about 10–15 minutes. Add the vanilla extract during the final minute of whipping.
Prepare the agar mixture: While the meringue is whipping, combine the water, granulated sugar, and agar powder in a small saucepan.Bring the mixture to a full boil, then continue boiling while whisking constantly for 2–3 minutes to fully activate the agar.
Incorporate the agar: Right before the agar mixture finishes boiling, stop the mixer and lower the bowl.As soon as the agar is ready, pour it all at once into the center of the meringue, avoiding the sides of the bowl. Raise the bowl and immediately begin mixing on low speed.Once the mixture looks fully incorporated, increase the speed to medium-high and continue whipping until evenly mixed.
Transfer and set: Working quickly, scrape the marshmallow mixture into the prepared pan and spread evenly.Let sit at room temperature for at least 2 hours, or until fully set.
Cut the marshmallows: Dust the top with more of the powdered sugar mixture. Turn the marshmallow slab onto a cutting board and cut into squares using a knife dusted with powdered sugar or cornstarch.Coat the marshmallows lightly to prevent sticking.
Notes
Store in an airtight container at room temperature, with layers separated by parchment paper to prevent sticking, for up to two weeks. Keep them away from humidity since agar-based marshmallows are more sensitive to moisture than gelatin-based ones and can become sticky in a humid environment.