Prep Pan: Grease a 9x13 pan* with butter or cooking spray. Evenly spread bread cubes throughout the pan.
Liquid Mixture: In a medium bowl, whisk together the eggs, milk, maple syrup, cinnamon, apple/pumpkin pie spice, salt, and vanilla until fully combined.
Soak: Pour mixture evenly over top of bread cubes, and press down lightly on cubes until they are soaked with the liquid. Cover tightly with plastic wrap or foil, and refrigerate overnight (or for a minimum of 4 hours).
Prep Oven: Once the casserole is ready to bake, preheat the oven to 350°F.
Cinnamon Drizzle: In a small bowl, combine melted butter with 1 tablespoon cinnamon and brown sugar and whisk until smooth. Drizzle mixture evenly over the top of the bread cubes.
Bake: Bake the casserole uncovered for 25-30 minutes, rotating halfway, until it is fully set in the middle and the top is toasted.
Cream Cheese Icing: In a small-medium bowl, microwave the cream cheese for 20-30 seconds until very soft to the touch. Add remaining ingredients and whisk until smooth. Consistency can be adjusted as needed with additional milk or powdered sugar. Cover and set aside until ready for use.
Finish: Once the casserole is removed from the oven, let cool in the pan on a wire rack and drizzle with cream cheese icing while still warm.
Store: Store cooled casserole and any leftover icing covered, in the refrigerator 4-5 days. Casserole can be covered and frozen after it is baked (without icing) in the freezer for 2-3 months and reheated in the oven until warm throughout.