Preheat the oven to 350 degrees F and grease a 9-inch cake pan (I like to use a springform pan for easy release, a pie dish works as well.) Set aside.
Mix the ground flaxseed and water in a small bowl and set aside to make your flax egg.
In a large bowl using a handheld mixer or a stand mixer with the paddle attachment, beat the softened vegan butter and brown sugar for 1-2 minutes until creamy.
Add the vanilla and the flax egg and mix to combine.
Next, stop the mixer and add the flour. Sprinkle the cornstarch, baking soda and salt on top of the flour. Turn the mixer on low speed, and mix until just combined.
Add in the chocolate chips to incorporate, either by hand or using the mixer.
Press the cookie dough evenly into the prepared pan. Bake for 25-30 minutes, until lightly golden brown. Let the cake cool completely if possible. You can serve it warm if you'd prefer.
If desired, pipe some frosting around the sides of the cookie cake. Alternatively, serve with vegan vanilla ice cream or coconut whipped cream. Top with more chocolate chips and serve.