Grease an oven-safe baking dish that fits your air fryer basket with butter or nonstick spray.
Place the bread cubes evenly in the prepared dish.
In a large bowl, whisk together the eggs, milk, heavy cream, sugar, vanilla, cinnamon, and salt until smooth.
Slowly pour the custard over the bread, pressing down gently so every cube soaks it up.
Cover and refrigerate at least 30 minutes, or overnight for best results.
Drizzle the melted butter over the top. Cover the dish loosely with foil and air fry at 320°F (160°C) for 12–15 minutes.
Remove the foil and air fry at 350°F (175°C) for 8–12 more minutes, until golden on top and set in the center (about 160°F internal; a knife inserted comes out mostly clean).
Let rest 5–10 minutes before serving. Finish with powdered sugar, maple syrup, or fresh fruit.