Place sugar, cornstarch, and salt in saucepan, and gradually whisk in coconut milk. Bring mixture to a boil over medium-low heat. Cook 5-10 minutes, or until thickened, whisking constantly. Turn off heat, stir in vanilla, then banana slices.
Line bottom of 11- x 7-inch baking dish with 24 cookies. Spread hot pudding over top, making sure bananas are submerged to prevent browning. Top with remaining 24 cookies, cover with plastic wrap, and cool. Refrigerate until cold. Top with whipped topping (if using).