In a large mixing bowl, whisk together the eggs, milk, vanilla, salt, cinnamon, and allspice until well combined.
Dip each slice of challah into the custard, letting it soak a few seconds per side to absorb the mixture.
Arrange the slices in a single layer in a greased air fryer basket or on a lined tray. Air fry at 350 degrees F for 8 minutes, flipping halfway through, until golden brown on both sides. Cook in batches if needed.
Meanwhile, melt the butter and brown sugar in a skillet over medium heat, stirring until smooth. Stir in the cinnamon and rum extract, if using.
Add the banana slices and cook for 3 to 5 minutes, turning gently once, until the bananas are softened and the sauce is syrupy. Watch closely so the sugar doesn't burn.
Plate the French toast, spoon the warm bananas and sauce over the top, and serve immediately.