Preheat the oven to 350°F (175°C). Lightly grease a 9-inch baking dish.
Spread the bread cubes in the dish and scatter the mashed bananas evenly over the top.
Whisk together the milk, eggs, sugar, brown sugar, vanilla, cinnamon, and salt. Pour this mixture over the bread and bananas. Let it sit for about 15 minutes so the bread can soak up the liquid.
Bake for 45-50 minutes or until the top is golden and the center is set. The edges should be slightly pulled away from the sides of the pan. A thin knife inserted into the center should come out clean.*
Notes
*If you'd prefer to check for doneness with a thermometer, aim for around 160°F (71°C).
Store in an airtight container in the refrigerator up to 4 days.