Banana Bread Pudding

12 ounces stale French bread, cut into cubes
4 large eggs
2 cups whole milk
1 cup (packed) dark brown sugar
½ cup unsalted butter, melted
¼ cup rum
2 teaspoons vanilla extract
1 teaspoon cinnamon
1/8 teaspoon salt
5 bananas, sliced into 1-inch-thick rounds

Directions
1. Preheat the oven to 375ºF. Lightly grease a 9-by-13-inch baking dish.

2. Place the bread in the prepared baking dish and spread it out in an even layer. Add the bananas and toss gently to mix.