Preheat oven to 350 degrees. Coat a 2 quart baking dish with non-stick cooking spray and set aside.
For the Bread Pudding:Place bread cubes on a rimmed baking sheet and bake until lightly toasted, 5 to 7 minutes.
In a bowl, combine the toasted bread cubes, apples and cranberries. In a large mixing bowl, whisk together the eggs, milk, cream, sugar, and vanilla. Pour over bread mixture and mix until well combined. Transfer to prepared baking dish.
Place baking dish inside a deep, large casserole dish or roasting pan. Fill larger pan with tap water about halfway up the sides of the baking dish. Bake at 350 degrees, checking periodically and adding more water if necessary. After 50 minutes, gently press down on the center of the pudding. If wet custard seeps to the top, let it bake for an additional 5 minutes or until a knife inserted near the center comes out clean.
For the Cream Sauce:Whisk together cream or half-and-half, cornstarch, and sugar, in a heavy saucepan. Cook and stir over medium heat until sugar is dissolved and mixture is just slightly thickened. Remove from the heat. Stir in the spiced rum (or extract) and nutmeg. Serve warm with pudding.