Spread Nutella on four slices of bread and top with remaining pieces of bread. Cut the sandwiches into 1/2-inch cubes.
In a large bowl, whisk together eggs, sugar and vanilla until very smooth. Stir in milk and add the bread. Let the mixture sit for 30 minutes, stirring occasionally.
Pour the mixture into the prepared pan. Bake until the pudding is set in the center, about 55 minutes. Let cool for 15 minutes. Slather the top with more Nutella, if desired. Bread pudding is best hot out of the oven, or refrigerated after a day. Microwaving it makes it rubbery.