Spread the bread cubes out on a baking sheet and let them sit for about 30 minutes to dry out slightly. If using fresh, soft bread, this step helps the cubes absorb the custard without turning to mush. Alternatively, you can use day-old bread.
In a large bowl, whisk together the eggs, milk, heavy cream, granulated sugar, vanilla extract, cinnamon, nutmeg, and salt until smooth and well combined.
Add the bread cubes and raisins to the custard mixture. Gently fold everything together, pressing the bread down so it soaks up the liquid. Let it sit for 10 minutes, giving it a gentle stir halfway through, until the bread has absorbed most of the custard.
Brush the melted butter inside a 6-inch round baking pan or oven-safe dish that fits in your air fryer. Pour the bread pudding mixture into the pan and press the top down gently with a spatula to even it out.
Preheat the air fryer to 320 degrees F. Place the pan in the air fryer basket and cook for 15 minutes. Check the center with a toothpick or knife.
If the center still looks very wet, cook for an additional 3 to 5 minutes until the top is golden and the custard is set but still slightly jiggly in the very center. Remove the pan from the air fryer and let it cool for 10 minutes. Dust with powdered sugar before serving. The bread pudding is wonderful on its own or with a drizzle of warm caramel sauce or a scoop of vanilla ice cream.