Prepare the bread by cutting it into 1-inch cubes and drying it out in the oven if necessary.

In a mixing bowl, whisk together the eggs, milk, heavy cream, sugars, vanilla, cinnamon, nutmeg, and salt until smooth.

Grease a baking dish with butter, add the bread cubes, and pour the custard mixture over them. Allow to soak for 15 minutes.

Preheat the oven to 350°F (175°C). Cover the dish with foil and bake for 30 minutes, then remove the foil and bake for another 15 minutes.

For the caramel, combine sugar and water in a saucepan over medium heat and stir until caramelized.

Remove the caramel from heat and carefully whisk in warmed heavy cream, butter, and vanilla until smooth.

Serve the warm bread pudding topped with the vanilla caramel sauce.