Preheat oven to 325°F and line a baking sheet with parchment paper.
In a bowl, whisk together the flour, baking soda, and cornstarch.
In another bowl, mix the softened vegan butter, brown sugar, and granulated sugar until smooth, about 1-2 minutes.
Add the applesauce and vanilla extract and stir until combined.
Add the dry ingredients and mix until a cookie dough forms.
Scoop dough into balls and place on the prepared baking sheet with space between each cookie.
Bake for 13 minutes, until the edges are lightly golden.
Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack.