Grease or spray crock of the slow cooker well. Prepare cake batter according to box directions. Pour prepared batter into slow cooker.
Cover slow cooker and set on HIGH. Cook for 2 to 3 hours, checking after 2 hours for doneness.
Remove crock from slow cooker and place on a cooling rack. Use the handle end of a wooden spoon to poke holes all over the cake, about an inch apart.
Whisk together pudding mix and cold milk. Pour pudding immediately over the cake (while it's still thin and hasn't had a chance to set) getting the pudding into each of the holes. Spread HALF of the can of Dulce de Leche over the pudding (you can warm it in the microwave to make it easier to spread). Place crock in the refrigerator for 1-2 hours.
Transfer remaining HALF of the can of Dulce de Leche to a medium bowl. Dulce de Leche is pretty thick so microwave it for 15-30 seconds to loosen it up. Add one tablespoon of the cream and stir. Continue thinning the Dulce de Leche with cream until it reaches a drizzling consistency.
When ready to serve, remove crock from refrigerator and cut cake into squares. Top each piece with Cool Whip and drizzle with thinned Dulce de Leche.