Heat the oven to 350 degrees and lightly grease a small baking dish.
In a mixing bowl, whisk together the milk, eggs, sugar, vanilla, cinnamon, and salt until smooth.
Add the bread cubes and sliced bananas to the bowl. Pour in the 1/2 cup dulce de leche and the melted butter. Stir gently until the bread is coated.
Transfer the mixture to the prepared dish and spread it evenly.
Bake for 35 to 40 minutes, until the top is golden and the center is set.
Remove from the oven and drizzle the remaining 2 tablespoons dulce de leche over the warm pudding before serving.