Preheat your oven to 350°F (175°C).

In a large mixing bowl, whisk together eggs, milk, half and half, brown sugar, pumpkin puree, vanilla extract, and pumpkin pie spice until smooth.

Cube the day-old French bread and gently fold it into the custard mixture until evenly coated. Let it sit for about 10 minutes.

In another bowl, mix together topping ingredients: brown sugar, flour, pumpkin pie spice, salt, and softened butter until crumbly.

Pour the bread mixture into a greased baking dish and sprinkle the topping over the top.

Bake for approximately 45 minutes or until golden brown and set in the center.

Allow to cool slightly before serving with maple syrup.