In a small saucepan, melt the butter over medium heat.
Add brown sugar and corn syrup, stirring until the mixture is smooth and bubbly.
Pour the mixture into a greased 9x13-inch baking dish and spread evenly.
Arrange the bread slices on top of the sugar mixture in a single layer.
In a large bowl, whisk together the eggs, half-and-half, vanilla, and salt.
Pour the egg mixture evenly over the bread.
Cover and refrigerate overnight.
Preheat the oven to 350°F (175°C).
Remove the casserole from the refrigerator and let stand at room temperature for 30 minutes.
Bake uncovered for 35-40 minutes or until puffed and golden.
Let cool slightly before serving.