Preheat oven to 350°F. Generously butter a 9 x 13-inch pan and set aside.
In a large bowl, mix eggs, milk, vanilla and sugar until smooth.
Layer bread on the bottom of the pan, followed by the bananas, nuts and chocolate chunks.
Pour the wet mixture into the pan making sure to evenly coat the bread. Press down with a spoon and let rest for 5 minutes until most of the liquid has been absorbed by the bread.
Bake for 45-50 minutes until the top is golden brown and the egg mixture is set in the middle.
Allow to cool for a bit before serving. Top with buttered rum sauce (optional).