Heat the brown sugar, butter, and corn syrup in a small saucepan over medium heat. Cook and stir until the mixture begins to boil; remove the mixture from heat, and pour into the prepared baking dish. Place the bread slices atop the brown sugar mixture.
Whisk the eggs and eggnog together in a large bowl; pour over the bread slices. Cover the baking dish with aluminum foil, and refrigerate 8 hours to overnight.
Preheat an oven to 325 degrees F (165 degrees C). Remove the baking dish from the refrigerator.
Bake in the preheated oven for 35 minutes. Increase heat to 375 degrees F (190 degrees C), remove the aluminum foil, and continue baking until the the top begins to brown, 5 to 7 minutes more.