Preheat the oven to 400 degrees F. Preheat a griddle to 350 degrees F or a nonstick skillet to medium heat.
Slice about 1/4-inch off the ends of the banana bread and discard. Cut the rest of the loaf into about 8 thick slices, about 1 and 1/4-inch thick each.
In a pie plate, or deep dish, whisk together the eggs, milk, vanilla, cinnamon, allspice and salt. Melt the butter on the griddle or skillet. Dip each slice of bread into the egg batter, one at a time, and place on the hot griddle. Cook each side of the bread slices for 1-2 minutes, until browned. Transfer to a baking sheet.
Bake all of the bread slices at once in the preheated oven for 12 to 15 minutes, until heated through and outer edges are crispy. Remove from the oven and serve immediately with syrup, whipped cream, powdered sugar, caramel sauce or whatever toppings you desire.