Grease a 9-by-13-inch (or other 14-cup) baking dish with the butter, then place the bread cubes in the pan and spread them into an even layer.
In a medium bowl or large measuring cup, combine the milk, eggs, brown sugar, vanilla, cinnamon and salt. Whisk until smooth.
Pour the custard mixture over the bread and press gently to help the bread absorb the liquid. Set aside, covered, for at least 30 minutes at room temperature, or up to 12 hours in the refrigerator.
Heat the oven to 400 degrees and let the casserole sit at room temperature while the oven heats. Meanwhile, make the topping: In a small bowl, mix the butter, brown sugar, cinnamon and salt with a fork until smooth.
Dollop the mixture all over the casserole, then gently spread it with the back of a spoon until the entire surface is covered. (If preparing the casserole the day prior to baking, don’t add the topping until just before it goes into the oven. Reheat the topping, if needed.)
Bake, uncovered, until puffed and golden brown, 30 to 35 minutes. Cut into squares, and serve hot. Top as desired.