Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper or a reusable silicone mat.

In a large mixing bowl with a hand mixer or stand mixer with the whip attachment, whisk the aquafaba and sugar for a full 4 minutes on high speed until frothy.

Add the coconut oil (or vegan butter), matcha powder, and vanilla extract. Continue to whip for 2 minutes until the mixture is smooth and thoroughly combined.

Sift in the flour, cornstarch, baking soda, and salt into the wet mixture, stirring until a soft dough forms.

Chill the dough for 30 minutes. Meanwhile, in a small bowl, mix the sugar and matcha powder for topping.

Scoop the dough into 2-tablespoon-sized portions and roll each into a ball. If using, press 4-5 mini-marshmallows into the center of each ball. Flatten the cookies in the palm of your hand and press the top of each cookie lightly in the sugar and matcha mixture. Place the sugar-coated cookie dough circles on the prepared baking sheet, spacing them 2 inches (5 cm) apart to allow for spreading.

Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden. The cookies will still be soft in the center but will firm up as they cool. Allow them to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely. Or serve them still a little warm if you made them with marshmallows inside.