In a large heavy-bottomed pot set over medium-low heat, add the butter, chocolate-hazelnut spread, and marshmallows. Stir until the mixture is completely melted and smooth. Stir in the vanilla extract.
Add the cereal and stir to coat completely, working quickly. Pour the mixture into the prepared baking dish. Use wet hands to press the mixture into an even layer. Set aside to firm up.
Frosting
In the bowl of a stand mixer fitted with the whisk attachment, add the softened butter and chocolate-hazelnut spread. Mix until smooth and well-combined.
Add the powdered sugar in batches and mix slowly at first until incorporated. Turn up the speed and mix until fluffy. Add the vanilla and the milk (or cream) and mix until smooth and spreadable. Add enough milk to achieve the desired consistency.
Spread the frosting evenly over the top of the Rice Krispie treats. Slice into larger bars (18-count) or smaller bars (24-count). Store in an airtight container. The bars will keep for 7 days.