Grease a 9-by-13-inch baking dish with butter or cooking spray.
Arrange the sliced bread in overlapping rows in the prepared dish.
Whisk the eggs, half-and-half, milk, granulated sugar, vanilla, custard cinnamon, custard nutmeg, and salt until smooth.
Pour the custard evenly over the bread, working some between the slices. Cover and refrigerate overnight.
The next day, heat the oven to 350°F and turn the bread slices once so they are evenly coated.
Mix the softened butter, brown sugar, corn syrup if using, topping cinnamon, and topping nutmeg. Spread the topping over the bread.
Bake uncovered for 35 to 40 minutes, until puffed and lightly golden.