01 - Preheat oven to 350°F. In a skillet over medium heat, melt the butter. Add brown sugar, cinnamon, nutmeg, and a pinch of salt, stirring until the sugar dissolves. Incorporate the diced apples and sauté, stirring frequently, for 5 minutes until just tender. Remove from heat and set aside.
02 - In a large mixing bowl, vigorously whisk the eggs, whole milk, heavy cream, granulated sugar, vanilla extract, and salt until fully combined. Layer the bread cubes and caramelized apples evenly in a 9×13-inch baking dish. Pour custard evenly over the mixture, gently pressing down to ensure the bread absorbs the custard. Allow the mixture to rest for 10 minutes.
03 - Transfer the baking dish to the oven and bake for 40 to 45 minutes, until the surface is golden and the center is set. A clean knife inserted near the center should emerge clean.
04 - As the pudding bakes, prepare the salted caramel. In a medium saucepan over medium heat, cook the granulated sugar, swirling the pan occasionally but not stirring, until it transforms into an amber liquid. Carefully add cubed butter; whisk continuously as the mixture bubbles vigorously. Gradually stream in the warm heavy cream, whisking constantly. Allow to boil for 1 minute, then remove from heat and stir in the sea salt. Cool slightly before serving.
05 - Cut the warm bread pudding into squares and transfer to serving plates. Generously drizzle each portion with the warm salted caramel sauce. Optionally, accompany with a scoop of vanilla ice cream or a dollop of whipped cream.