Preheat the oven to 375°F/190°C and make sure the oven racks are in the middle of the oven for the best air circulation. Prep 3 baking trays with parchment paper or a silicone non-stick baking mat of your choice. Set them aside.
Make the flax egg. In a small mixing bowl, whisk together the flaxseeds with hot water and set it aside for about 5 minutes. This allows the flaxseeds to get gel-like to hold the cookies together.
Mix the wet ingredients. In the large bowl with the hand mixer, or in the stand mixer with the paddle attachment, mix together the softened vegan butter and peanut butter with both white and brown sugars. Mix this until it is well combined and fluffy, about 3 minutes on medium speed. Add the flax seeds and the vanilla.
Add the dry ingredients. After the wet ingredients are well mixed, start to add the dry ingredients. Add the baking powder, baking soda, cornstarch, salt, and all-purpose flour. Mix this on a low setting until the dough is formed.
Shape the cookies. Scoop the cookies with a one tablespoon scoop and roll them in the extra white sugar. Place them on lined baking sheets and taking the backside of a fork, press the criss-cross pattern into the top of them.
Bake the cookies. Bake a single tray of cookies at a time for 13 to 15 minutes or until the cookies are golden brown on the edges.
Cool and enjoy! Remove the cookies from the oven and let them rest for 10 minutes on the hot trays before removing them to wire racks to finish cooling. Enjoy!