Prep the bread. Cut bread into ¾-inch cubes. If bread is fresh, leave cubes uncovered on the counter for 2 hours or toast at 300°F for 5 minutes.
Whisk the custard. In a wide bowl, whisk eggs, milk, vanilla, cinnamon, brown sugar, and salt until completely smooth.
Soak. Add bread cubes to the custard. Toss gently to coat. Let sit 2–3 minutes, tossing once. No pooled liquid should remain.
Butter toss. Drizzle melted butter over cubes and toss to coat evenly.
Air fry. Line basket with air-fryer parchment or spray well with oil. Arrange cubes in a single layer with space between each. Cook at 370°F for 8–10 minutes, shaking the basket at the 5-minute mark, until deeply golden and crisp on the outside.
Serve immediately. Dust with powdered sugar and serve with warm maple syrup and berries.