Spray a 4-quart baking dish with nonstick cooking spray. Cut loaf slices into 1-inch cubes and place in baking dish.
In a large mixing bowl, combine eggs, milk, pumpkin, brown sugar, vanilla extract, cinnamon, pumpkin pie spice, and salt, and whisk until well combined. Evenly pour egg mixture over bread cubes and press down gently. Cover with plastic wrap and refrigerate for three hours or up to overnight.
In a medium-sized bowl, use a fork to combine butter, flour, brown sugar, granulated sugar, pumpkin pie spice, and kosher salt. Mixture should be dry, with various sizes of crumbs to form the streusel. Refrigerate separately from casserole.
Before baking, let casserole and streusel set at room temperature for about an hour. Adjust oven rack to middle position and preheat oven to 350℉. Sprinkle streusel all over casserole, cover with foil, and bake covered for 30 minutes. Uncover and bake for another 20 minutes. Serve with warm maple syrup.