Combine ingredients for cake batter. Pour into prepared cake pans and bake. Let cakes cool. Place cakes in fridge while ice cream is in freezer.
Add milk, cream, and sugar to bowl and combine. Pour into ice cream maker and churn. When almost finished, add crushed Oreos and Nutella. Spoon ice cream into lined cake pan, smooth top, and refreeze. Once ice cream has hardened, assemble cake and top with Nutella!