Drain pineapple, reserving juice for later.
Place pineapple in paper towel and squeeze to remove excess moisture. Set pineapple aside.
Place carrots in paper towel and squeeze to remove excess moisture. Set carrots aside.
Preheat oven to 350.
Heavily grease 9x13" baking pan. Set aside.
Combine cake mix, oil, vanilla, 1/2 cup of reserved pineapple juice and eggs in a large bowl.
Beat until combined.
Fold in shredded carrots and 1 cup of crushed pineapple that has had moisture removed.
Transfer to prepared pan.
Bake 30 minutes or until toothpick inserted in center comes out clean.
After cake has cooled for about 5 minutes, poke large holes into the cake (I use the end of a wooden spatula).
Allow to finish cooling.
In a small bowl, combine cheesecake pudding and milk.
Whisk until combined.
Immediately spread across cake. Use a spatula to force pudding mixture into holes.
Chill for about 30 minutes.
In a medium bowl, combine whipped topping and remaining crushed pineapple that has had moisture removed.
Spread whipped topping mixture on top of cake and refrigerate for an additional 30 minutes.