Preheat your oven to 350°F (175°C) and grease a 9x13 inch baking dish.
In a large bowl, whisk together eggs, milk, cream, sugars, vanilla, cinnamon, nutmeg, and salt until well combined.
Add the bread cubes to the custard mixture and gently toss to coat. Let sit for 15 minutes to absorb the liquid.
In a separate bowl, toss the chopped apples with 2 tablespoons of brown sugar and 1/2 teaspoon of cinnamon.
Layer half of the soaked bread cubes in the prepared baking dish. Top with half of the apple mixture. Repeat with the remaining bread and apples.
Pour any remaining custard over the top of the bread and apples.
Cover the dish with foil and bake for 30 minutes.
Remove the foil and bake for an additional 15-20 minutes, until the top is golden brown and the custard is set.
While the pudding is baking, prepare the caramel sauce. In a medium saucepan, melt the butter over medium heat. Add the brown sugar and stir until dissolved.
Add the cream and salt, stirring constantly. Bring to a simmer and cook for 5 minutes, until slightly thickened.
Remove the bread pudding from the oven and let it cool for 10 minutes.
Drizzle the warm caramel sauce over the bread pudding just before serving.