Brown sausage in a large skillet over medium, crumbling it; drain excess fat and set aside to cool.
Whisk eggs, milk, garlic powder, salt, and pepper in a large bowl until combined.
Grease a 9x13-inch dish; layer bread, sausage, broccoli, onion, and cheese evenly inside.
Pour egg mixture over everything; press gently to soak all bread. Cover tightly with foil; refrigerate overnight.
Next morning, preheat oven to 350°F. Bake covered 30 minutes; uncover and bake another 15 minutes until golden and center is set.