Dry the bread. Spread the cubes on a baking sheet and leave them out for a few hours, or bake them at 350 degrees F for 10 to 15 minutes until dry but not toasted. Dry bread is what holds its shape instead of turning to mush.
In a large bowl, whisk together the eggs, yogurt, milk, 1/2 cup granulated sugar, 1 teaspoon cinnamon and the nutmeg until smooth.
Stir in the apples and the raisins, then gently fold in the bread cubes until every piece is coated.
Spray a 9x13 baking dish with cooking spray and pour in the mixture. Press the bread down into the custard with the back of a spoon, then let it stand 30 minutes at room temperature, pressing down once more halfway through. This soak is what turns the cubes into custard instead of dry bread, so do not skip it. You can also cover the dish and refrigerate it overnight at this point.
Heat the oven to 350 degrees F. Stir together the 2 tablespoons sugar and 1 teaspoon cinnamon and sprinkle it over the top.
Bake 45 to 55 minutes, until the top is golden and puffed and the center is set. A knife slipped into the middle should come out clean. If the top browns before the center sets, tent it loosely with foil. Straight from the refrigerator, add 5 to 10 minutes.
While it bakes, make the sauce. In a heavy saucepan over medium heat, melt the butter, then whisk in the brown sugar, heavy cream and salt.
Bring it to a gentle boil, whisking the whole time, then cook 5 to 8 minutes until it coats the back of a spoon. Keep whisking, because that is what holds the butter and cream together. Take it off the heat and stir in the vanilla. It thickens more as it cools.
Let the bread pudding rest 10 minutes, then pour the warm caramel over the pan or spoon it over each serving. Vanilla ice cream on top is not optional in this house.