Spray a 9x13-inch baking dish with cooking spray. Preheat your oven to 350°F.
In a large bowl, whisk together the eggs, milk, heavy cream, granulated sugar, brown sugar, vanilla extract, and gingerbread spice until well combined.
Add the bread cubes to the egg mixture and toss until all the bread is well-coated and the liquid is absorbed. Let it sit for a few minutes to ensure the bread absorbs the custard.
In a small bowl, mix together the flour, brown sugar, gingerbread spice, and salt. Using a fork or pastry cutter, work the butter into the mixture until it resembles coarse crumbs.
Pour the soaked bread mixture into the prepared baking dish, spreading it out evenly. Sprinkle the crumb topping evenly over the bread mixture.
Bake for 45 minutes, or until the top is golden and crispy and the center is set and no longer wet.
If desired, dust with powdered sugar using a fine mesh strainer before serving. For best results, this dish is best enjoyed right away!