Mix eggs, milk, butter, vanilla extract, and cinnamon together in a bowl.
Line an air fryer basket with parchment paper. Dip each piece of bread into the milk mixture and place in the basket. Make sure they are not touching; cook in batches if necessary.
Preheat the air fryer to 370 degrees F (188 degrees C). Add basket and cook bread for 6 minutes; flip and cook for 3 minutes more. Sprinkle each stick with confectioners' sugar.
