Melt the butter in a small pan over low heat. Mix in the brown sugar and cinnamon. Spread the mixture evenly on the bottom of a 9 x 13 baking dish. Top with two layers of bread, packed tightly together. In a bowl, whisk together eggs, salt, vanilla, and milk. Pour evenly over the bread. Cover with plastic wrap and refrigerate overnight or for at least 8 hours.

Bake at 350 degrees until puffed and golden brown, about 45 minutes. Let cool for 10 minutes before serving, turning each piece upside down with the brown sugar mixture on top.