In a big bowl, mix the eggs and sugar, beating until the sugar dissolves completely.
Beat in the butter. Then add in the milk, cream, mashed banana, salt, cinnamon, nutmeg and vanilla until well combined.
Grease with butter a rectangular pound cake pan and place the bread pieces in it, then pour the previous mixture over the bread. Let it sit for 30 minutes to 1 hour in the refrigerator.
Preheat the oven to 375°F (180°C) for 10 minutes. Once this time has passed, bake the pudding for 40 minutes aprox.