Preheat the oven to 300 degrees Fahrenheit.
If using a food processor, place the aquafaba in the bowl and run it on high speed, with the feed tube open, for about five minutes. The quantity of liquid is too small for it to splash through the open feed tube and on you, but if you wish hold a kitchen towel over the mouth of the feed tube for a few seconds until the aquafaba starts to get foamy. You can also whip your aquafaba and continue making the dough in a stand mixer or with bowl and a hand mixer.
When the aquafaba starts to firm up and holds soft peaks when you pick it up with a spoon, add the powdered sugar, 1/4th cup at a time, pulsing for a few seconds after each addition, until all of the sugar is incorporated.
Now you can just dump in the remaining ingredients -- the almond flour, gluten-free flour, baking powder, and vanilla and almond extracts. Close the lid and pulse for a few seconds or until the dough comes together.
Remove the blade carefully from the food processor bowl. Prep a cookie sheet by spraying lightly with oil or by covering the bottom with parchment paper.
Place the sugar for rolling in a dish.
Use your fingers to take a small piece of dough and roll it into a ball, about 3/4 inch in diameter. Roll the ball of cookie dough in the sugar and then place it on the cookie sheet. Press lightly on the top to flatten a little.
Do this with the remaining dough. You will get around 18 cookies. Place the cookies at least an inch apart on the baking sheet.
Bake in the preheated oven for 30 minutes or until the bottoms are golden-brown.
Remove the baking sheet to a rack and allow the cookies to cool at least 10 minutes before sliding them off the cookie sheet. Let the amaretti cookies cool completely on a rack.