Preheat oven to 350 degrees F. Spray a 9x13-inch glass baking dish with cooking spray; set aside.
In a large bowl, whisk together milk and pudding mix for 2 minutes; let stand for 3 minutes until thick.
In a large mixing bowl, beat cake mix, water, oil, and eggs with an electric mixer on low speed for 30 seconds. Scrape down sides of bowl; beat for 2 minutes on medium speed. Stir in butterscotch chips and carrot. Pour batter into prepared dish. Pour pudding over batter; spread evenly.
Bake in preheated oven for 35 to 40 minutes or until cake tester inserted in center comes out clean. Serve cake warm with a scoop of vanilla ice cream.