In a small saucepan melt butter with brown sugar and corn syrup over moderate heat, stirring, until smooth, and pour into a 13 by 9 by 2-inch baking dish. Slice bread and trim crust if desired. Arrange slices in one layer in baking dish, squeezing them slightly to fit. In a bowl whisk together eggs, half and half, vanilla, and salt until combined well, and pour evenly over bread. Chill bread mixture, covered, at least 8 hours and up to 1 day.

Preheat oven to 350 degrees and bring bread mixture to room temperature. Bake uncovered, in middle of oven until puffed and edges are golden, 35 to 40 minutes.