Butter a 9 x 13-inch baking dish (or a tall-sided 12-inch ovenproof skillet) and arrange the cubed bread in the dish.
In a big bowl, whisk the eggs to combine, then whisk in the heavy cream, milk, rum, brown sugar, vanilla, cinnamon, nutmeg, and salt until smooth. Pour the mixture over the bread, really pressing down on the bread to help the custard soak in. Cover with plastic wrap and refrigerate for at least 6 hours and up to 12.
Heat the oven to 350°F. Take the casserole out of the fridge and let it sit at room temp for 30 minutes.
Make the topping: In a bowl, combine the cereal, melted butter, and salt and toss to coat. Spread the mixture evenly over the casserole.
Bake until the topping is golden and the bread cubes peeking out of the top are crusty and toasty, 50 to 55 minutes. Serve warm with maple syrup.