Preheat your oven to 350°F (175°C) and grease a baking dish.

In a large mixing bowl, whisk together the eggnog, milk, sugar, eggs, vanilla extract, cinnamon, nutmeg, and salt until well combined.

Add the cubed bread to the eggnog mixture and gently toss until every piece is coated. Let it sit for 10 minutes.

Pour the mixture into the prepared baking dish and bake for 35-40 minutes until the edges are set.

While the pudding bakes, combine eggnog, sugar, and cornstarch in a saucepan and heat until thickened.

In a separate bowl, beat the egg and temper it with a bit of the hot mixture before combining back.

Remove from heat and stir in butter and spiced rum, then keep warm until serving.