Begin by cutting day-old bread into 1-inch cubes, which will allow for better custard absorption. Grease a 9x13-inch baking dish with butter or cooking spray. Evenly distribute the bread cubes in the dish.

In a large mixing bowl, whisk together the eggs, milk, pumpkin puree, sugar, vanilla extract, cinnamon, and nutmeg until thoroughly combined. Pour the custard evenly over the bread cubes.

Gently press down on the bread cubes to help them absorb the custard mixture. Allow to soak for at least 15-20 minutes at room temperature, or cover and refrigerate for at least 2 hours or overnight.

In a separate bowl, beat the softened cream cheese with powdered sugar until smooth. Once the custard has set, dollop spoonfuls of the cream cheese mixture over the soaked bread.

Preheat your oven to 350°F (175°C) and cover the baking dish with aluminum foil. Bake for 30 minutes, then remove the foil and bake an additional 15-20 minutes until the top is golden brown.

Remove from oven and let it cool for about 10-15 minutes. Slice into squares and serve warm, dusting with powdered sugar or drizzling with maple syrup.