Sift together the powdered sugar and cornstarch; use a portion to coat the bottom and sides of an 8x8 inch square baking pan.

Place aquafaba and cream of tartar in a stand mixer fitted with a whisk attachment; beat on high speed until stiff, glossy peaks form (approximately 10 minutes).

Combine granulated sugar, water, and agar-agar powder in a small saucepan over medium heat.

Whisk the sugar mixture constantly and bring to a boil; continue cooking until the mixture reaches 240°F (115°C) on a candy thermometer.

Set the stand mixer to low speed and slowly drizzle the hot sugar syrup into the whipped aquafaba in a thin, continuous stream.

Increase the mixer speed to high and whip for 5 to 8 minutes until the bowl feels cool to the touch and the mixture is very thick.

Fold in the vanilla extract during the last minute of whipping.

Transfer the mixture to the prepared pan and smooth the surface with a greased spatula.

Allow the marshmallows to set at room temperature for at least 4 hours.

Dust the top with the remaining starch-sugar mixture, turn out onto a cutting board, and slice into 24 cubes.

Toss individual cubes in the starch-sugar mixture to prevent sticking.