Preheat the oven to 350°F. Cut the french bread into 1-inch cubes and spread out on a baking sheet. Bake the bread cubes for 5 to 7 minutes. The bread cubes should be dried but not browned. Spray a 13×9 inch baking pan with non-stick spray and set aside.
In a mixing bowl, whisk together the eggs, eggnog, whole milk, sugar, rum, nutmeg, and salt. Transfer the bread cubes to the baking dish. Pour the egg custard over the bread cubes. Gently toss the bread with your hands to makes sure it is evenly coated. Let sit for a minute then gently toss the bread cubes again to ensure they have evenly soaked up the egg custard.
Sprinkle the raw turbinado sugar over the bread cubes. Bake for 40 to 45 minutes until a knife inserted in the middle of the bread pudding comes out clean.
Hot Buttered Rum Sauce
In a saucepan, melt the butter over medium heat. Add the brown sugar and heavy cream to the saucepan and whisk until the sauce is fully emulsified. Bring the sauce to a simmer and let cook for 2 to 3 minutes. Whisk in the rum, spices, and kosher salt and remove from the heat. Allow the sauce to cool before using. The sauce will thicken as it cools.
To serve, top the bread pudding with warm hot buttered rum sauce and enjoy!
Notes
*To make this alcohol free, substitute each tablespoon of rum with 1 teaspoon of rum extract.