Preheat oven to 350°F. Spray a 9x13-inch baking dish with cooking spray.
In a large bowl, whisk together eggs, milk, garlic powder, smoked paprika, salt, and pepper.
Layer the cubed bread evenly in the prepared baking dish. Top with pulled pork, bell peppers, onion, and 1½ cups of cheese.
Pour the egg mixture evenly over everything, pressing down gently to ensure the bread soaks up the liquid.
Cover with foil and refrigerate for at least 2 hours or overnight (or freeze at this point for later use).
Bake covered for 30 minutes, then remove foil, sprinkle remaining ½ cup cheese on top, and bake uncovered for 15 more minutes until golden and set.
Let stand 10 minutes before serving. If frozen, thaw overnight in refrigerator before baking, adding 10-15 minutes to cooking time.