Preheat your oven to 375°F. Grease a 2-quart casserole dish to ensure your pudding doesn’t stick.
Place the cubed bread into the greased casserole dish and drizzle the melted butter evenly over the top, tossing to coat.
In a medium bowl, lightly beat the eggs. Add the milk, sugar, vanilla, cinnamon, nutmeg, and salt, whisking until combined. Gently stir in the banana slices.
Pour the custard mixture over the bread cubes. Use a spatula to press down and ensure all bread is soaked in the custard.
Bake the dish, uncovered, for 40 minutes or until a knife inserted in the center comes out clean. The top should be golden brown.
While baking, prepare the sauce. In a small saucepan, melt butter over medium heat. Stir in the sugar and cornstarch mixture until well combined.
Slowly whisk in the milk and corn syrup, stirring continuously. Bring the mixture to a full boil and boil for 1 minute, then remove from heat. Stir in the vanilla extract.
Serve the bread pudding warm, drizzled generously with the prepared sauce.