Prepare cake mix according to package instructions for a 13- x 9-inch cake; stir in shredded apple to the batter. Bake cake for 20 minutes. Remove from oven and let cool.
Meanwhile, place apple juice in a medium saucepan over medium-high heat; bring to a boil. Allow juice to boil undisturbed until it is reduced by more than half and has thickened somewhat.
Combine 1 tablespoon cornstarch with 1 tablespoon water to form a slurry; whisk into gently boiling juice and whisk until thickened. Remove from heat. Carefully stir in butter, vanilla and salt. Allow mixture to cool slightly.
Using round handle of a wooden spoon, poke holes over entire top of cake surface, being careful not to poke through to bottom of pan.
Pour cooled sauce over surface of cake, filling in holes and allowing sauce to soak into cake. Let cake stand at room temperature for about 30 minutes.
Spread whipped topping evenly over top of cake and sprinkle with crushed cookies. Store in refrigerator.