Preheat oven to 350°F and grease a 9×13 baking dish.
In a large bowl, whisk yogurt, milk, eggs, cinnamon, nutmeg, and sugar.
Stir in apples and raisins, then fold in bread cubes. Pour into dish.
Mix cinnamon and sugar in a small bowl; sprinkle over top.
Bake for 30–40 minutes until golden and puffed.
Meanwhile, heat butter, cream, and brown sugar in a saucepan. Bring to a boil, then simmer 5 minutes until thickened.
Drizzle sauce over baked pudding and top with vanilla ice cream.