In the bowl of a stand mixer, use the paddle attachment to cream together the softened coconut oil, sugars, egg, and vanilla extract on medium-high speed until light and fluffy, about 3 minutes.
Add in the flour, cornstarch, baking soda and salt, and beat on medium-low speed until combined. Fold in (stir in) the chocolate chips by hand until just combined.
Use a large cookie scoop (equivalent to 3 tablespoons) or a spoon to shape the dough into balls, and place them on a large plate. Cover with plastic wrap and chill the dough balls for at least 2 hours.
When you are ready to bake the cookies, preheat oven to 350 degrees F. Place chilled dough balls at least 2 inches apart on a parchment-lined baking sheet. (Or a baking sheet that has been covered with a Silpat, or greased with cooking spray.)
Bake for 10-12 minutes until the edges are just set. The centers may look slightly undercooked. Cool cookies on the baking sheet for about 5 minutes, then transfer to a wire rack to finish cooling. Serve immediately or store in a sealed container for up to 1 week. You can also freeze the cookies for up to 3-4 months.