Preheat the oven to 350°F. Line a large baking tray with parchment paper.
In a small pot over low heat, melt the coconut oil. Stir in the chocolate and cocoa powder, whisking just until melted. Set aside so it can come to room temperature.
In the bowl of a stand-mixer with a bubble whisk attachment, or in a medium-sized bowl with electric beaters, beat the aquafaba until it has thickened and holds a sloped bird beak shape when the whisk is dipped into the aquafaba and lifted, about 5-8 minutes. Add in the sugar and vanilla, beating until well combined, another minute or so. Pour in the cooled chocolate mixture, beating for another minute.
In a small bowl, sift the flour, cornstarch, baking powder, and salt together. Add the flour mixture to the rest of the ingredients and beat until well blended. Place the batter in the fridge for 45 minutes to let it firm up a bit and not be sticky. It will not be like regular cookie dough, but will resemble very thick chocolate fudge.
To form the cookies, take 2 tbsp worth of dough (use a cookie scoop if you have one), and roll into a ball. Place the balls on the cookie tray leaving about 2 inches between each cookie. Using a measuring cup or the palm of your hand, press down each ball until it is about 1/2" thick (they will spread during baking).
Bake the cookies for 9-11 minutes, checking at 9 minutes to make sure you aren't over baking them. Sprinkle lightly with the coarse salt, if desired, part way through baking. Let the cookies cool for 5 minutes on the cookie tray before moving to a cooling rack (they will be fragile when they first come out of the oven.) Enjoy!