First,dd the room temperature vegan butter and sugar to a bowl and cream together until fluffy, about 2 minutes. Then add the oat milk and vanilla to the mixing bowl and mix together for another 30 seconds.
Next, add the flour, cornstarch, baking powder, and salt to the mixing bowl. Make sure to add the flour first and then pile the other ingredients on top. Then, mix together until a smooth and thick cookie batter forms.
Add the bowl of cookie dough to the fridge, cover, and let chill for 30 minutes- 1 hour.
Cover a baking sheet in parchment paper and preheat the oven to 350F. Next, remove the dough from the fridge and use a large cookie scoop to form 7 large cookies. Roll into balls between your palms until the cookie dough balls are round.
Place the sugar cookie dough balls onto the baking sheet and lightly press the dough down with your palm to flatten. Make sure that each cookie is kept about 2 inches apart since they will spread while baking.
Bake for 12-15 minutes until bottoms are lightly browned and the cookie is cooked through but has slightly soft centers. The cookies will continue baking after they are removed from the oven so the centers should still be soft, not glossy or raw, when they are removed from the oven. If you would like to make smaller cookies (about 10 vs 7) make sure to adjust the baking time to 10-12 minutes.
Let the cookies cool on the baking sheet for 5 minutes. Then, transfer to a wire rack to continue cooling.