Preheat the oven to 350ºF or 180ºC, and line 2 large baking sheets with parchment paper. Set aside.
Prepare the flax egg by mixing the ground flaxseed with the water, and let the mixture rest at room temperature for at least 5 minutes.
Add the vegan butter, granulated sugar, and brown sugar to a large bowl and beat until light and fluffy using a hand mixer or a stand mixer fitted with a paddle attachment.
Add the vanilla and flax egg and beat on low speed until just incorporated.
Add the flour, cornstarch, baking soda, and salt, and beat on low speed until combined.
Add in the vegan chocolate chips to incorporate, either by hand or using the mixer. If the dough is too sticky to work with, place it in the refrigerator and chill for 30 minutes.
I used a cookie scoop to make my cookies, but feel free to use a regular spoon or even your hands.
Fill the scoop with dough and just press and release onto the prepared baking sheets, about 2 inches apart from each other (about 5 cm).
Bake for 10-12 minutes or until the cookies are lightly golden brown. They will be soft when they come out of the oven but will firm up as they cool.
Remove from the oven and allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a cooling rack to cool completely.