Preheat oven to 325 degrees F (165 degrees C). Grease a 9x13-inch baking dish.
Spread bread cubes on a baking sheet and bake until crisp, about 20 minutes.
Meanwhile, melt butter in a skillet over medium heat. Saute apples until tender, 7 minutes, then transfer to prepared baking dish along with bread. Toss to combine.
Whisk together sugar, cinnamon, and salt in a large bowl. Whisk in whole eggs and yolks until well combined, then whisk in milk, cream, and vanilla. Pour mixture evenly over bread mixture. Let stand, covered, 45 minutes at room temperature.
Preheat oven to 325 degrees F (165 degrees C).
Bake pudding until bread has absorbed custard and is set, about 50 minutes.