Unless your bread is already fairly dry, you'll want to toast the bread before making the casserole. Spread the bread cubes on a rimmed baking sheet and toast them for 4 minutes, just until the outsides firm up a bit. Remove the bread, but leave the oven on.
Place the bread cubes in the pan. In a large bowl, whisk together the eggs, milk, cream, sugar, vanilla, cinnamon, and salt. Add the mashed bananas. Pour about ¾ of the custard over the bread cubes in the pan and let sit for about 5 minutes so that the bread absorbs some of the liquid. Pour the rest of the custard over the top.
Transfer the bread pudding to the pan and bake for about 50 minutes, until the pudding sets and the top is golden brown. Let sit on a wire rack for 15 to 20 minutes until it firms up a bit but is still warm. Serve warm with whipped cream or vanilla ice cream if desired.
Notes
Dry Bread Cubes for Banana Bread Pudding
It may seem counterintuitive, but the best bread for bread pudding (and stratas and stuffing) is bread that is slightly stale. Dry bread absorbs the custard and any liquid the recipes call for more easily, while soft, moist bread will simply get leaden and soggy.If your bread is fresh, and you don’t have time to wait for it to dry out, you can simply toast the cubes in the oven. Cut the bread into cubes, and spread them out on a baking sheet. Toast the bread cubes in a 300-degree oven for about 10 minutes until they get a bit crusty and dry.