Line two baking sheets with silicone baking mats or parchment paper. Set aside.

Place the coconut oil, brown sugar, granulated sugar, nondairy milk, and vanilla extract in a medium bowl. Whisk until smooth and combined.

Add the flour, cornstarch, baking soda, and salt to the bowl. Mix with a rubber spatula until a smooth dough forms. Fold in the chocolate chips.

Divide the cookie dough into 20 balls, using roughly 1 1/2 tablespoons of dough for each, and arrange them spaced 1 1/2 inches apart on the baking sheets. Transfer the sheets to the freezer for 10-15 minutes. Alternately, freeze the dough balls on a small tray or large plate, then transfer to the baking sheets after freezing.

Preheat the oven to 350°F.

Bake the cookies on middle rack of oven until puffy and golden brown at the edges, 14-16 minutes.

Check to see that cookies are done. Remove from oven or add time as needed.

Allow the cookies to rest on the sheets for 5-10 minutes, then transfer to a wire rack to cool completely before serving.