In a mixing bowl, whip together vegan butter and brown sugar until smooth. Vigorously whisk up the aquafaba until nice and frothy, then add to the bowl along with vanilla and whisk again.
Sift in flour, baking powder, baking soda and salt, then use a spatula to gently fold into the wet mixture until batter is smooth. Fold in dark chocolate chunks and transfer this mixture into the refrigerator while you prepare the mochi filling.
In a small, microwave safe bowl, whisk together flour, cornstratch, sugar and milk until smooth. Tightly cover with plastic wrap, leaving a small opening on one side of the bowl to allow steam to escape. Microwave for 30 seconds.
Remove from the microwave and use the spatula to stir in between. Return to the microwave for another 30 seconds and repeat once more, for a total of 3 rounds in the microwave. The mixture should be mochi-like and pull away from the sides of the bowls. If not, return to the microwave and repeat once more.
Finally, add vegan butter to the mixture and use the spatula to incorporate into the mochi. It may take a little bit of effort but will eventually work its way into the mochi.
Transfer the mochi to a nonstick baking mat or nonstick surface and divide the mochi into 12 pieces. I found that working with about a tablespoon and a half of mochi works best and you may end up with a little bit of mochi leftover.
Take the cookie dough out of the fridge and scoop 2-3 tablespoons of dough into your hand. Press a piece of mochi into the center and wrap the dough around the mochi to ensure it's completely covered. Transfer the stuffed dough ball onto a nonstick baking mat lined baking sheet and repeat until all the dough has been used.
Transfer the baking sheet to the fridge for at least an hour, or preferably overnight.
Once ready to bake, preheat the oven to 375F. Leave a generous amount of space between each cookie, roughly 4 inches, and lightly press down the balls of dough before baking.
Bake for about 15-20 minutes, until edges are golden brown and sprinkle with flaky salt while hot, if desired. Keep in mind the cookie will continue to bake once pulled from the oven, as it cools. These are larger cookies, so it will feel like you're baking them for longer than usual.