Coat a 9"x13" baking dish thoroughly with some of the softened butter or with cooking spray to prevent sticking. Slice the French bread into 1-inch thick slices and arrange them in the prepared baking dish in rows, overlapping the slices slightly. Set this aside while preparing the custard.

In a large bowl, whisk the eggs until well beaten. Add the half and half, milk, granulated sugar, vanilla extract, 1/2 teaspoon ground cinnamon, 1/2 teaspoon ground nutmeg, and salt. Continue whisking until the mixture is smooth and fully combined.

Pour the custard mixture evenly over the arranged bread slices, making sure each slice is thoroughly coated. Spoon some of the mixture between the slices to ensure all parts of the bread are saturated. Cover the dish with foil and refrigerate overnight to let the bread absorb the custard.

Preheat the oven to 350°F. Before baking, flip each piece of bread over in the dish so everything is well coated with the custard. In a medium bowl, combine the remaining softened butter, light brown sugar, light corn syrup, 1 teaspoon ground cinnamon, and 1/2 teaspoon ground nutmeg. Mix until smooth and well combined—I find using room temperature butter makes spreading much easier.

Spoon the prepared topping mixture evenly over the soaked bread slices, spreading it like icing over the surface and in between the slices as desired. Bake uncovered for 35–40 minutes, or until the French toast is puffed and lightly golden. Allow it to cool slightly before serving for the best texture. For an even richer flavor, I sometimes finish with a sprinkle of extra cinnamon just before serving.