Preheat oven to 350 degrees. Spray a 2- to 2½-quart quart baking dish with nonstick cooking spray. Set aside.
In a Dutch oven, bring squash, onion, 3 cups water, and broth to a boil. Reduce heat to medium-low; simmer until squash is crisp-tender, approximately 7 minutes. Drain well.
In a large bowl, gently stir together squash mixture, ½ cup cheese, sour cream, mayonnaise, butter, salt, pepper, garlic powder and egg. Spoon half of squash mixture into prepared dish, spreading evenly. Sprinkle with half of crushed crackers. Top with remaining squash mixture, remaining crushed crackers and remaining cheese.
Bake until cheese melts, approximately 25 minutes.